Effects Of System Rotation Research Articles

Hydrodynamic instability of flow through a rotating channel filled with isotropic porous media

Various geophysical and engineering applications have underlying physics, comprising system rotation's effects on the dynamics and transport phenomena in porous media flows. Comprehensive knowledge of the instability in a rotating fluid-saturated porous layer is beneficial for controlling the transport phenomena and the mixing process. The present study focuses on the temporal evolution of small disturbances in a pressure-induced fluid flow through a spanwise rotating channel filled with an isotropic porous material. A Darcy–Brinkman model, including the Coriolis force term in the momentum equation, is employed to describe the developed flow. A normal mode analysis is performed, and the coupled Orr–Sommerfeld–Squire eigenvalue problem is formulated to capture the linear instability of the perturbed flow. The Chebyshev collocation technique is used to solve the fourth-order eigenvalue problem to capture the transient behavior of the finite-amplitude disturbances. The temporal growth rate and marginal stability curves related to the Coriolis force-based instabilities are investigated. The rotating porous media flow is unstable at a much lower Reynolds number than the non-rotating configuration. The analysis confirms co-existing unstable modes and mode coalescence for a specific range of parameters, which can enhance the mixing and transport inside the porous layer. The neutral stability curves show the appearance of two different unstable zones corresponding to the long and moderate waves. Moreover, the higher permeability and porosity of the porous medium have a destabilizing influence.

Effects of system rotation on turbulent structure of inhomogeneous stably stratified flow

Effects of system rotation on turbulent structure of inhomogeneous stably stratified flow

A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow

Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.

Effects of system rotation on turbulent structure of inhomogeneous stably stratified flow

Effects of system rotation on turbulent structure of inhomogeneous stably stratified flow

Computational Fluid Dynamics Study of Separated Flow Over a Three-Dimensional Axisymmetric Hill

This paper investigates the ability of computational fluid dynamics (CFD) simulations to accurately predict the turbulent flow separating from a three-dimensional (3D) axisymmetric hill using a recently developed four-equation eddy-viscosity model (EVM). The four-equation model, denoted as k–kL–ω–v2, was developed to demonstrate physically accurate responses to flow transition, streamline curvature, and system rotation effects. The model was previously tested on several two-dimensional cases with results showing improvement in predictions when compared to other popularly available EVMs. In this paper, we present a more complex 3D application of the model. The test case is turbulent boundary layer flow with thickness δ over a hill of height 2δ mounted in an enclosed channel. The flow Reynolds number based on the hill height (ReH) is 1.3 × 105. For validation purposes, CFD simulation results obtained using the k–kL–ω–v2 model are compared with two other Reynolds-averaged Navier–Stokes (RANS) models (fully turbulent shear stress transport k–ω and transition-sensitive k–kL–ω) and with experimental data. Results obtained from the simulations in terms of mean flow statistics, pressure distribution, and turbulence characteristics are presented and discussed in detail. The results indicate that both the complex physics of flow transition and streamline curvature should be taken into account to significantly improve RANS-based CFD predictions for applications involving blunt or curved bodies in a low Re turbulent regime.

On the turbulent heat transfer in a square duct subjected to spanwise system rotation

In this paper, direct numerical simulation is performed to study the effects of the Coriolis force on turbulent heat transfer within a square duct subjected to spanwise system rotation. In order to investigate the influence of system rotation on the heat transfer process, a wide range of rotation numbers have been tested. In response to the system rotation, mean secondary flows appear as large streamwise counter-rotating vortices, which interact intensely with the four boundary layers of the square duct and have a significant impact on the statistics of the coupled velocity and temperature fields. It is observed that at a sufficiently high rotation number, heat convection approaches a complete laminarization state near the top and side walls. The influence of large organized secondary flows on the transport of the turbulent scalar energy of the temperature field has been analyzed in both physical and spectral spaces. The effects of system rotation on the turbulent heat fluxes have been examined through a budget analysis of their transport equations. The role of near-wall streamwise-elongated turbulence structures on heat transfer is studied using a linear stochastic estimation approach. It is observed that the near-wall ejection events are amplified by the system rotation, resulting in a strong negatively-valued vertical turbulent heat flux in the near-wall region.

Numerical simulations of rotating bubble plumes in stratified environments

AbstractThe effects of system rotation on the turbulent dynamics of bubble plumes evolving in stratified environments are numerically investigated by considering variations in both the system rotation rate and the gas‐phase slip velocity. The turbulent dispersion of a passive scalar injected at the source of a buoyant plume is strongly altered by the rotation of the system and the nature of the buoyancy at the source. When the plume is driven by the density defect associated with the presence of slipping gas bubbles, the location of the main lateral intrusion decreases with respect to the single‐phase case with identical inlet volume, momentum, and buoyancy fluxes. Enhanced downdrafts of carrier phase fluid result in increased turbulent mixing and short‐circuiting of detraining plume water that elevate near‐field effluent concentrations. Similarly, rotation fundamentally alters dynamic balances within the plume leading to the encroachment of the trapping height on the source and an increase in turbulent dispersion in the near field. System rotation, even at modest Rossby numbers, produces a sustained, robust, anticyclonic precession of the plume core. The effects of rotation and the presence of bubbles are cumulative. The vertical encroachment of the primary intrusion and the overall dispersion of effluent are greatest at smallest Rossby numbers and largest slip velocities. The main characteristic feature in rotating single‐phase plumes, namely the robust anticyclonic precession, persists in bubble plumes. Analysis of the momentum budgets reveal that the mechanism responsible for the organized precession, i.e., the establishment of an unstable vertical hydrostatic equilibrium related to radial cyclostrophic balance, does not differ from the single‐phase case.

Sensitization of a Transition-Sensitive Linear Eddy-Viscosity Model to Rotation and Curvature Effects

A new scalar eddy-viscosity turbulence model is proposed, designed to exhibit physically correct responses to flow transition, streamline curvature, and system rotation effects. The eddy-viscosity model (EVM) developed herein is based on the k–ω framework and employs four transport equations. The transport equation for a structural variable (v2) from a curvature-sensitive Shear Stress Transport (SST) k–ω–v2 model, analogous to the transverse turbulent velocity scale, is added to the three-equation transition-sensitive k–kL–ω model. The physical effects of rotation and curvature (RC) enter the model through the added transport equation. The new model is implemented into a commercial computational fluid dynamics (CFD) solver and is tested on a number of flow problems involving flow transition and streamline curvature effects. The results obtained from the test cases presented here are compared with available experimental data and several other Reynolds-Averaged Navier-Stokes (RANS) based turbulence models. For the cases tested, the new model successfully resolves both flow transition and streamline curvature effects with reasonable engineering accuracy, for only a small increase in computational cost. The results suggest that the model has potential as a practical tool for the prediction of flow transition and curvature effects over blunt bodies.

Effects of System Rotation on Vortical Structure in Wall Turbulence

Direct numerical simulations (DNSs) of rotating turbulent Poiseuille flows are performed to study the effects of both cyclonic and anticyclonic system rotation on the kinematics of the quasi-streamwise vortices. By using the second invariant of the deformation tensor, a number of streamwise vortices are detected and averaged in the wall vicinity where the intense sweep motion, i.e., the inrush motion of high-speed fluid toward the wall, is related to the quasi-streamwise vortices. The effects of the system rotation on the angle of vortex axis are clearly observed as studied in longitudinal vortices of the homogeneous shear flow. Moreover, by calculating the probability of the emergence of the counterclockwise vortices (CCVs) around a clockwise vortex (CV), we find that with increase in the anticyclonic system rotation, the probability increases and decreases in the ejection and sweep sides of a CV, respectively. In contrast, cyclonic system rotation attenuates CCVs in both sides of a CV, though it increases at the top of the CV. This distribution of CCVs is found to affect sweep motion related to the quasi-streamwise vortices.

Numerical investigation of monodisperse granular flow through an inclined rotating chute

A discrete element model of spherical glass particles flowing down a rotating chute is validated against high quality experimental data. The simulations are performed in a corotating frame of reference, taking into account Coriolis and centrifugal forces. In view of future extensions aimed at segregation studies of polydisperse granular flows, several validation steps are required. In particular, the influence of the interstitial gas, a sensitivity study of the collision parameters, and the effect of system rotation on particle flow is investigated. Shirsath et al. have provided the benchmark laboratory measurements of bed height and surface velocities of monodisperse granular flow down an inclined rotating chute. With a proper choice of the friction coefficients, the simulations show very good agreement with our experimental results. The effect of interstitial gas on the flow behavior is found to be relatively small for 3‐mm granular particles. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3424–3441, 2014

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates Ω is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of Ω = 5 rad/s (with Rossby number much smaller than unity). Typically, the Taylor-scale Reynolds number in our experiments is around Reλ ≈ 100. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see L.J.A. van Bokhoven, H.J.H. Clercx, G.J.F. van Heijst, and R.R. Trieling, Experiments on rapidly rotating turbulent flows, Phys. Fluids 21 (2009) 096601. Based on the full set of velocity derivatives, measured in a Lagrangian way by three-dimensional (3D) particle tracking velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. For the range of rotation rates considered, the experimental results show how the turbulence evolves from almost isotropic 3D turbulence (Ω ≲ 0.2 rad/s) to quasi-two-dimensional turbulence (Ω ≈ 5.0 rad/s), and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect of background rotation is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.

Experimental study of monodisperse granular flow through an inclined rotating chute

In blast furnaces, particles like coke, sinter and pellets enter from a hopper and are distributed on the burden surface by a rotating chute. Such particulate flows suffer occasionally from particle segregation during transportation caused by differences in density or size. To get a more fundamental insight into these effects, we started an experimental study to investigate the effect of rotation on such particulate flows. Here, as a first step, we present an experimental study of granular flow of monodisperse 3 mm spherical glass particles flowing with a constant mass rate through a rotating smooth rectangular chute, which is inclined at a fixed angle. Experiments are performed for a sufficiently long time to study steady (but streamwise accelerating) flow. Particle image velocimetry (PIV), electronic ultrasonic height sensors, and a dynamic weighing scale are used to measure the surface velocity of the particle stream, the particle bed height and mass flow rate in the chute, respectively. The influence of rotation speed and angle of inclination of the chute is studied. We find an interesting interplay between the Coriolis force, which pushes the granular flow to the sidewall of the chute and tends to diminish the acceleration of the flow, and centrifugal forces that accelerate the flow. The velocity components display a complex dependence on the spanwise and streamwise position in the chute. The bed height in the chute is also influenced by these effects of system rotation. These measurements provide a well-defined set of observations for refining and validating computer simulations of granular flows, and point out some important limitations of physical experiments. We present preliminary three-dimensional discrete particle simulations, which show that the experimental measurements of bed height and surface particle velocity in a chute inclined at 30° can be predicted nearly quantitatively both without and with rotation of the chute.

Modeling the Effects of System Rotation on the Turbulent Scalar Fluxes

A proposal for modeling the effects of system rotation on the turbulent scalar fluxes is presented. It is based on extension to rotating frames of an explicit algebraic model derived using tensor-representation theory. The model is formulated to allow for the turbulent scalar fluxes to depend on the details of the turbulence field and on the gradients of both the mean-velocity and the scalar. Such dependence, which is absent from conventional models, is required by the exact equations governing the transport of the scalar fluxes. The model’s performance is assessed, both a priori and by actual computations, by comparisons with results from recent direct numerical simulations (DNS) of flows in heated channels rotated about their streamwise, spanwise, and wall-normal axes. To place the new model’s performance in context, additional comparisons are made with predictions obtained from three alternative models, namely, the conventional gradient-transport model, a model that is implicit in the scalar fluxes derived by simplification of the modeled transport equations for the scalar fluxes, and a differential scalar-flux transport model. The results show that the present model yields predictions that are substantially in better agreement with the DNS results than the algebraic models, and which are indistinguishable from those obtained with the more complex differential model. However, important differences remain and reasons for these are discussed.

Computer Experiments on Rapidly Rotating Plane Couette Flow

Turbulent flows in rotating frame-of-reference are of considerable interest in a variety of industrial, geophysical and astrophysical applications. In these flows, the system rotation induces additional body forces, i.e. centrifugal and Coriolis forces, acting on the turbulent flow, so that the momentum mechanism becomes more complicated. The present doctoral thesis concerns the system rotation influence on turbulent shear flows. To this end, direct numerical simulations (DNSs) have been performed in order to investigate the effect of system rotation on different turbulent flow configurations including plane Couette flow, sudden expansion flow and wake behind a flat plate. In addition, the PIV measurements for rotating plane channel and sudden expansion flows have been carried out in order to support the numerical simulations results. A realistic turbulent inflow boundary condition is needed in order to perform direct numerical simulations for spatially developing flows subjected to system rotation such as rotating sudden expansion flows. The cost effective method is introduced based on a separate (precursor) simulation in order to establish fully turbulent inflow including wide ranges of length and time scales needed in the direct numerical simulations. On the other hand, the characteristic features of the rotating turbulent flows were investigated by means of three-dimensional flow visualization, two-point correlations and transport for the individual second-moments of the velocity and vorticity fluctuations.

Objective Model for the Fluctuating Pressure-Strain-Rate Correlations

Representation theorems for isotropic functions are used to construct a closure model for the fluctuating pressure-strain-rate correlation tensor. In contrast to alternative proposals in the literature, the present model does not include a dependence on the vorticity in inertial frames or on the intrinsic spin tensor in noninertial frames because it is shown that this dependence violates objectivity which has been previously suggested to be an essential property of a turbulence closure. The proposed model is calibrated using data from homogeneous shear flows in inertial frames and is tested against data from a variety of turbulent shear flow, in both fixed and rotating frames, with generally very encouraging results. In particular, the results conclusively demonstrate that the absence of dependence on vorticity and intrinsic spin in the model for the pressure-strain-rate correlations does not adversely impact its ability to accurately predict the effects of system rotation on the turbulence.

Capturing Effects of Rotation in Sudden Expansion Channels Using Detached Eddy Simulation

T HE effects of system rotation are of interest in flows in hydro/ turbo machinery especially in the design of centrifugal compressor impellers and runner blades. When the direction of rotation is in tandem with the fluid rotation vector, that is, the vorticity, the flow is stabilized, whereas the flow is destabilized if the directions are opposing. As with boundary layers, shear layers are also stabilized or destabilized by rotation. Rotation (or streamline curvature) generates extra strain rates that significantly affect turbulent stress production. Bradshaw [1] formulated an analogy between meteorological parameters and parameters describing rotation about the axis normal to the plane of rotation. He defined an effective Richardson number (Ri) for flows undergoing rotation that is used to define amodifiedmixing length [l l0 1 Ri ].Most of the later studies also propose a similar definition, where the effects of rotation are modeled by formulating corrections using a rotation Richardson number. Nilsen and Andersson [2] used an algebraic second moment closure model to predict the rotational effects on backward facing step flows. It was observed that rotation induced variation in the mean flow pattern was a result of significant changes in turbulent fluctuations in the free shear layer. However quantitative predictions of the reattachment length showed only partial agreement with the experimental data (Rothe and Johnston [3]). A similar study was carried out on rotating flows using a v–f model by Iaccarino et al. [4]. Both the original and a modified version of the model were used to predict the reattachment length downstream of a backward facing step. The modified model predicted the reattachment length better than the originalmodel. However itwas observed that the predictions of the modified model, like the algebraic second moment (ASM) model of Nilsen and Andersson [2] showed only partial agreement with the experiments. Therefore in spite of the continual development of Reynolds-averagedNavier–Stokes (RANS)models, predicting the effects of rotation in turbulent flows is a major challenge. The eddies formed in themassively separated regions downstream of the step are geometry specific. The “detached” eddies are not as universal as the eddies in typical thin shear layers where RANS models are calibrated. This is the reasonwhyRANSmodels are often observed to fail in flows undergoing massive separation. Large eddy simulation (LES) resolves the large energy carrying eddies while modeling the smaller isotropic eddies using a subgrid scale stress model. LES is a viable and a reliable method for simulating flows undergoing massive separation. However the near-wall resolution necessary for LESmakes it prohibitively expensive at high Reynolds numbers. A solution to the computational challenges associated with the reliable prediction ofmassively separated turbulent flows is detached eddy simulations (DES). DES sensitizes a RANS model to grid length scales, thereby allowing it to function as a subgrid scalemodel in critical regions of interest. This allows the natural instabilities of the flow in this region to develop, the energy cascade to grow, and improves the quality of the solution in this region. Though DES was initially proposed for the Spalart–Allmaras model, it can be easily extended to other models (Strelets [5]), by appropriately defining a turbulent length scale. The credibility of the approach has been validated by numerous applications in the literature for external and internal flows. The objective of the current study is to investigate the capabilities of DES in capturing the effects of rotation induced Coriolis forces on turbulent separation and reattachment in a backward facing step geometry. To evaluate the accuracy of the scheme in predicting the effects, the reattachment lengths predicted by DES are compared with experimental measurements by Rothe and Johnston [1] and also compared with other RANS models from the literature.

Study of Boundary Layer Flow in Rotating Curvature System (Effects of System Rotation on Occurrence and Growth of Goertler Vortices)

The behavior of the boundary layer in rotating channels, such as that in impeller passages of turbomachinery, is dominantly influenced by the centrifugal and Coriolis forces due to the wall curvature and system rotation, respectively. The resultant force may promote or suppress the instability in the boundary layer, depending on its magnitude of the component normal to the wall boundary. The purpose of the present study is to make clear experimentally the effects of Gortler type instability on the laminar boundary layer developing along the concave surface, focusing attention on transition process from laminar to turbulent state in the rotating system with streamline curvature. The longitudinal velocity and turbulent intensity have been measured near the concave surface in the channel whose radii of center line curvature is 1000 mm. When the Coriolis force acts toward the concave wall due to the channel rotation, the occurrence of the Gortler vortices shifts upstream and the vortex structure is maintained in more downstream sections. In the earlier stage of vortex development an oscillation of flow was found to appear in the vortices irrespective of the rotating condition.

Effects of Helicity and System Rotation on Decaying Homogeneous Turbulence.

To consider the nonreflection property of the turbulence statistics in a rotating system, a new method has been proposed to introduce turbulence helicity into an isotropic turbulent field for direct numerical simulation (DNS). Effects of the helicity and the rotation on turbulence statistics and vortex structure are investigated by theoretical analysis and DNS of the homogeneous decaying turbulence. Although DNS results show that both rotation and the helicity inhibit energy decay, theoretical analysis reveals the occurrence of very different mechanisms for the rotation and the helicity for producing the inhibition effect. The helicity directly decreases the energy transfer while the rotation suppresses the energy transfer due to the so-called scrambling effect. The other effect of system rotation is that rotation elongates the vortex structure along the rotation axis, however, the presence of the helicity appears to weaken this tendency.

Effect of System Rotation on Energy Transfer of Homogeneous Decaying Turbulence.

The effect of system rotation on energy spectrum, energy transfer function and triadic energy transfer function is investigated using the DNS data of homogeneous decaying turbulence subjected to system rotation. The DNS is performed with 128 Fourier modes at various rotation rate up to 50[rad/s]. The initial Taylor micro-scale Reynolds number is 53.6. The results of this study are summarized as follows : (1) The profile of the energy spectrum approaches the linealized solution with an increase in the rotation. That is, the decay of the energy spectrum is inhibited and promoted in low and high wave number regions, respectively, by the rotation. The absolute value of the energy transfer function decreases with an increase in the rotation. This phenomena is explained by scrambling effect. (2) The rotation gives the directional anisotropy on the energy spectrum and energy transfer function. However the effect of the directional anisotropy on the energy spectrum becomes negligible when the rotation rate is too high. (3) The triadic energy transfer is also prevented by the rotation. The local energy transfer is dominant in the non-local triad for both rotating and non-rotating systems. The rotation also gives the directional anisotropy on the triadic energy transfer function.

Effects of System Rotation on Turbulence.

Effects of System Rotation on Turbulence.