Streamwise Rotation Research Articles

Vortex-shedding modes of a streamwise and transversely rotating sphere undergoing vortex-induced vibrations

We investigate the vortex-shedding modes of a streamwise and transversely rotating sphere undergoing vortex-induced vibration (VIV). At Reynolds number Re = 500, we have conducted direct numerical simulations for reduced velocities U∗=6,8, and 11, considering dimensionless streamwise (αx) and transverse (αz) rotation rates set at αx,z=1. At αx=1, the vortex-shedding mode exhibits twisted spiral-like structures, while at αz=1, ring-like structures form through the stretching and twisting of hairpins. For αx=1, the dimensionless circulation (Γx) decreases with increasing U∗, showing negative growth at U∗=6. Conversely, for αz=1, Γx remains negative except at U∗=8, where counterclockwise vortex rotation results in positive circulation. At αz=1, VIV is periodic for U∗=6 and 8 but intermittent at U∗=11. Phase analysis using the Hilbert transform reveals anti-phase synchronization in the phase between the sphere's displacements and the vortex force coefficient (ΔϕV) and phase slip in the phase between the sphere's displacements and the total force coefficient (ΔϕT) along the y direction for αx=1. At αz=1, phase slip with distinct phase-locking epochs is observed along the z direction for all U∗ cases. Pre-lock-in behavior with phase slip is also noted for U∗=11 along the y direction.

Effects of streamwise rotation on helicity and vortex in channel turbulence

Helicity plays a key role in the evolution of vortex structures and turbulent dynamics. The helicity dynamics and vortex structures in streamwise-rotating channel turbulence are discussed in this paper using the helicity budget equation and the differentiated second-order structure function equation of helicity. Generally, rotation and Reynolds numbers exhibit opposing effects on the interscale helicity dynamics and the vortices. Under the buffer layer, the positions of the helicity peaks are proportional to the ratio between the Reynolds and rotation numbers. The mechanism is related to the opposing effects of convection and rotation. Rotation directly affects the helicity balance through the Coriolis term and corresponding pressure term. In the buffer layer, the scale helicity is negative at small scales but positive at large scales, which is mainly induced by the spatial effects (the production and the spatial turbulent convection) but reduced by interscale cascades. Examination of structures reveals the close association between scale helicity and streaks, with streak lift angles exhibiting an increase with rotation and a decrease with Reynolds numbers. In the log-law layer, the Coriolis terms and corresponding pressure terms are proportional to the rotation numbers but remain independent of the Reynolds numbers. The negative scale helicity is forward cascaded towards small scales. Generally, spanwise vortices in the log-law layer are related to sweep events and forward cascades. Our findings indicate that these spanwise vortices are suppressed by rotation but recover with increasing Reynolds numbers, aligning with the effects observed in the scale helicity balance.

On the origin of streamwise vortices in braid regions for compressible mixing layers

The origin of initial streamwise vortices in braid regions and their relationship with deformed spanwise vortices are numerically studied via direct numerical simulation (DNS) in the compressible mixing layer with a convective Mach number (Mc) of 0.4. Through an analysis of fast Fourier transform on DNS data, two low-rank velocity models (vd and vs) are developed to demonstrate that both deformed spanwise vortices and streamwise vortices are all originated from the linear superposition of a fundamental norm mode [mode (1, 0)], a pair of fundamental oblique modes [modes (1, ±1)], and a mean mode. Further investigations reveal that, downstream of spanwise vortices, the increase in amplitude ratio (Ao/An) between modes (1, ±1) and mode (1, 0) leads to the formation of deformed spanwise vortices in vortex regions. As the amplitude ratio Ao/An further increases, reaching the threshold that the streamwise rotation motion from modes (1, ±1) exceeds the spanwise irrotational deformation from mode (1, 0), streamwise vortices are generated in braid regions. The aforementioned formation path for deformed spanwise vortices and streamwise vortices provides a mechanism support for our flow visualization results that the emergence of deformed spanwise vortices precedes that of streamwise vortices in the flow field.

Wake instability behind a streamwise and transversely rotating sphere

The wake instabilities associated with a streamwise and transversely rotating sphere at very high rotational speeds are not clearly understood. This article attempts to address typical wake instability characteristics when the sphere rotates along the streamwise and transverse directions through direct numerical simulations. We have found that a larger streamwise rotation makes the wake bifurcate into large-scale shear-layer structures. In contrast, the azimuthal stretching during transverse rotation splits the wake into a twin jet-type flow pattern, resulting in the transverse expansion of the wake.

Helicity budget in turbulent channel flows with streamwise rotation

The streamwise rotation effects in turbulent channel flows are reflected not only in the appearance of the secondary flows but also in the weakened streamwise velocity and spanwise vorticity. In this paper, we investigate the secondary flows from three perspectives: the mean spanwise velocity, the mean streamwise vorticity, and combined mean and fluctuating helicity. We found that the combined helicity is also an alternative perspective to characterize the streamwise rotation effect, especially for the secondary flows. The budget equations of the mean and fluctuating helicity in physical space are derived theoretically and analyzed numerically. The streamwise rotation effects on the secondary flows are directly reflected on the pressure and Coriolis terms, which provides an essential source for helicity within the near-wall regions. The production term could be decomposed into two terms, which originate from the momentum and vorticity equations, respectively. The helical stress (velocity–vorticity correlation) originating from the vorticity equation shows a simple profile distribution and is dominant for the production for the helicity within the near-wall regions. The high helical structures in the core regions can be explained as an intense wall-normal transportation, which transfers produced helicity within the near-wall regions into the core regions.

Helicity distributions and transfer in turbulent channel flows with streamwise rotation

Helicity is a quadratic inviscid conservative quantity in three-dimensional turbulent flows and is crucial for turbulent system evolution. Helicity effects have mainly been highlighted over the past few decades to explore the intrinsic mechanism of turbulent flows, while the statistical characteristics of helicity itself are nearly absent in general anisotropic turbulent flows. In this paper, we investigate the helicity statistics in turbulent channel flows with streamwise rotation at moderate rotation numbers ($Ro_{\tau }=7.5,15$and 30) and Reynolds numbers ($Re_{\tau }=180$and 395), including their spatial and scale distributions, anisotropy and cross-scale transfer. The appearance of a mean secondary flow in the spanwise direction corresponds to a mean streamwise vorticity, which indicates the presence of a high-helicity distribution. Numerical results reveal a regular helicity profile along the wall-normal direction, and a new peak is found in the near-wall region around$y^+=6$of the streamwise or spanwise helicity profiles. The inter-scale helicity transfer is analysed by the filtering method, and the numerical consequences reveal that the second channel of the helicity cascade we proposed previously is dominant in contrast to the first channel. The rotation effects are explored by comparing the numerical results obtained under different rotation numbers. With increasing rotation number, more helical structures in the near-wall regions are present, with peaks of helicity profiles and fluxes coming closer to the wall. With a higher Reynolds number, their amplitudes are larger and scale-space transfer is strengthened. These systematic numerical analyses uncover the helicity distributions and transfer in wall-bounded turbulent flows.

A Bayesian approach to the mean flow in a channel with small but arbitrarily directional system rotation

The logarithmic law of the wall loses part of its predictive power in flows with system rotation. Previous work on the topic of mean flow scaling has mostly focused on flows with streamwise, spanwise, or wall-normal system rotation. The main objective of this work is to establish the mean flow scaling for wall-bounded flows with small but arbitrarily directional system rotation. Our approach is as follows. First, we apply dimensional analysis to the Reynolds-averaged momentum equation. We show that when a boundary-layer flow is subjected to small system rotation, the constant stress layer survives, and the mean flow U+ is a universal function of y+, Ωx+, Ωy+, and Ωz+, where U is the mean flow, y is the distance from the wall, Ωi is the system rotation speed in the ith direction (in the locally defined coordinate), and the superscript + denotes normalization by the local wall units. Second, we survey the three-dimensional parameter space of Ωx,y,z+ and determine U+(y+,Ωx+,Ωy+,Ωz+) for small Ω+. Here, we conduct direct numerical simulation (DNS) of a Reτ = 180 channel at various rotation conditions. This approach is conventionally considered as “brutal force.” However, as we will show in this work, the Bayesian approach allows us to very efficiently sample the parameter space. Four independent surveys are conducted with 146 DNSs, and the resulting Bayesian surrogate agrees well with our DNSs. Finally, we upscale to high Reynolds numbers via wall-modeled large-eddy simulation. In general, the present framework provides a path for surrogate modeling in a high-dimensional parameter space at high Reynolds numbers when sampling in a designated parameter space is possible at only a few conditions and at a low Reynolds number.

Coherent structures in streamwise rotating channel flow

Direct numerical simulation and large-eddy simulation are employed to study the effects of streamwise rotation on turbulent channel flow, especially the coherent structures. Two Reynolds numbers (Re = Umh/ν = 2800 and 7000) with a wide range of rotation numbers (0 ≤ Ro = 2Ωh/Um ≤ 7.5) are considered, where Ω denotes the angular velocity of the system and Um and h are the bulk velocity and one-half of the channel height, respectively. The demand on the streamwise computational domain size increases as the rotation number increases. Flow statistics are presented and discussed. Among the near-wall quasi-streamwise vortices rotating in opposite directions, the rotation of the channel tends to promote the cyclones (vortices rotating in the same direction as the channel) and suppress the anti-cyclones, which is visualized by the conditional-sampling method. Elongated large-scale vortices, which typically form in rotating homogeneous turbulence, are observed through the conditional-sampling method. Similar to the columnar vortices in homogeneous turbulence, the elongated large-scale vortices are dominated by cyclones at Ro ∼ 1, while the dominance becomes less apparent as the rotation number further increases. When rotation is suddenly imposed to fully developed turbulent flow, the integral scale along the rotating axis increases linearly at a growth rate proportional to the rotation number. What is interesting is that the cyclones of the large-scale vortices are not completely elongated along the rotating axis but slightly tilted to the spanwise direction. The cyclones prefer to develop in the lower and upper half channels, while the anti-cyclones, if they exist, occur in the central region of the channel. This preference of the large-scale vortices in different regions contributes to the secondary flow. It is revealed that the mean shear of the channel flow may have effects on the tilting of the large-scale vortical structures and the preference of their distributions in the channel.

Wake characteristics of a sphere performing transverse rotary oscillations

Abstract Three-dimensional computations have been carried out to investigate flow past a sphere performing rotation and rotary oscillation about streamwise axis. The effect of streamwise rotation has been analysed for fixed Reynolds number of 300, with non-dimensional rotational rate taking values 0, 0.5, 1, 1.5 and 2. The transitions in the near wake have been depicted with the help of time-averaged path lines, iso- λ 2 surfaces and vortex core transformation. This study is further extended by considering forced rotational oscillations of the sphere for two different amplitudes of oscillation and reduced oscillation frequency ranging from 0.5 to 2. Effect of these parameters on flow structure has been described using λ 2 -surfaces and streamlines at different locations in the flow field. The response of mean hydrodynamic forces to variation in amplitude and frequency of oscillation has also been reported. Temporal behaviour of wake has been disclosed through Hilbert spectral analysis of time dependent force coefficient signals. The growth and evolution of wake nonlinearities have been elaborated with the help of marginal spectra, Hilbert spectra and distribution of non-stationarity.

Wake characteristics of a sphere performing streamwise rotary oscillations

Three-dimensional computations have been carried out to investigate flow past a sphere performing rotation and rotary oscillation about streamwise axis. The effect of streamwise rotation has been analysed for fixed Reynolds number of 300, with non-dimensional rotational rate taking values 0, 0.5, 1, 1.5 and 2. The transitions in the near wake have been depicted with the help of time-averaged path lines, iso-λ2 surfaces and vortex core transformation. This study is further extended by considering forced rotational oscillations of the sphere for two different amplitudes of oscillation and reduced oscillation frequency ranging from 0.5 to 2. Effect of these parameters on flow structure has been described using λ2-surfaces and streamlines at different locations in the flow field. The response of mean hydrodynamic forces to variation in amplitude and frequency of oscillation has also been reported. Temporal behaviour of wake has been disclosed through Hilbert spectral analysis of time dependent force coefficient signals. The growth and evolution of wake nonlinearities have been elaborated with the help of marginal spectra, Hilbert spectra and distribution of non-stationarity.

Development of secondary flow field under rotating condition in a straight channel with square cross-section

The developing secondary flow fields in the entrance section of a rotating straight channel were experimentally investigated using Particle Image Velocimetry (PIV). The effects of streamwise position, Reynolds number and rotation number on the development of the secondary flow fields were revealed. The results show that the absolute values of vorticity flux of the trailing side roll cells increase with increasing radius of the measured plane and rotation number. When the absolute value of vorticity flux exceeds a critical value, the merging of the trailing side roll cells appears. Moreover, when the number of the trailing side vortex pairs is even, the absolute values of vorticity flux of the leading side vortices increase along streamwise direction. Otherwise, the absolute values decrease along the streamwise direction. By the circulation analysis, this phenomenon was found to have relationship with the merging of the trailing side roll cells, and further concluded that the secondary flow field in a rotating channel has to be treated as a whole. At last, the increase of the Reynolds number was found to be able to induce the merging position moves upstream.

1079 NUMERICAL INVESTIGATION FOR HOMOGENEOUS TURBULENT FLOW WITH UNIFORM SHEAR UNDER STREAMWISE ROTATION

In this study, the direct numerical simulation (DNS) for homogeneous shear turbulence in the system rotating along the streamwise direction is fulfilled. Due to the rotation effect, the turbulence energy becomes small during the initial short time and the Reynolds shear stress are suppressed more strongly with increasing the system angular velocity. Since the redistribution related to the rotation and pressure-strain terms of the Reynolds normal stress is weakened by the streamwise rotation, the anisotropy of the normal stresses is strengthened. In the strong rotation case the anisotropy of the velocity spectra is strong in the whole wavenumber region in contrast with the isotropy of the nonrotating case in the large one. From the viewpoints of the probability density function (PDF) for the vorticity vector angle and visualization for the vortex structure, we find that the vortex structures become large and stand in a line by the streamwise rotation axis. Moreover, we suggest that the rapid distortion theory (RDT) simulation reproduces the rotation effect on the mean quantities of the DNS results in only short time immediately after a calculation start.

Effects of streamwise rotation on the dynamics of a droplet

An initially streamwise rotating droplet released into a uniform cross flow is studied numerically. The computations are performed using a finite volume Navier–Stokes solver which employs a moving mesh interface tracking scheme to locate the interface. With a large initial Weber number (Wei = 40) the streamwise rotating droplet flattens along the free stream direction more quickly as rotation rate (\documentclass[12pt]{minimal}\begin{document}$\varOmega ^*$\end{document}Ω*) increases, and leads to a dramatic increase in the dynamic drag coefficient (CD/A*, where A* is the dimensionless frontal area). On the other hand, for Wei = 4 and 0.4 at \documentclass[12pt]{minimal}\begin{document}$\varOmega ^* \ge 0.6$\end{document}Ω*≥0.6, the flattening of the droplet is less pronounced and the droplet even restores to spherical shape, hence, CD/A* decreases sharply. The dynamic drag coefficient even becomes negative for Wei = 4 and 0.4 at \documentclass[12pt]{minimal}\begin{document}$\varOmega ^* = 1$\end{document}Ω*=1. At the largest deformation, the droplet can be classified into three major shapes: biconvex, convex-concave, and biconcave. One dominant feature of the wake downstream of the droplet is the formation and convection of vortex rings. The shape and deformation of the droplet is dependent not only on the size of the vortex ring, but also upon the free stream dynamic pressure and droplet pressure. The detachment of vortex ring in the wake leads to a substantial drag reduction, and this detachment occurs at Re ≈ 28.

G050043 主流方向系回転一様剪断乱流の直接数値計算

Direct numerical simulation (DNS) for homogeneous shear turbulence in the system rotating along the streamwise direction by means of the remeshing pseudo-spectral method is fulfilled. The increase rate of the turbulence energy is suppressed and the anisotropy of the Reynolds stresses is strengthened due to the rotation effect. In the strong rotation case, the anisotropy of the velocity spectra is strong in the large and small wavenumber regions. The vortex structures become large and stand in a line by the streamwise rotation.

G050021 主流方向に系回転するMHD一様勇断乱流の直接数値計算([G05002]流体工学部門一般セッション(2):複雑流)

The direct numerical simulation for MHD homogeneous shear turbulence under the streamwise system-rotation isperformed. There are small differences for the kinetic and magnetic energy, Reynolds and Maxwell stresses in theseveral streamwise rotation cases by comparison with the results of the spanwise rotation MHD field. Immediately afterthe calculation start, however, the contribution of the energy transformation becomes large as the rotation increases.From the kinetic energy spectral budget it is found that the sum of the transfer and transformation spectral functions isbalanced with the dissipative one in the small scale.

Helical-wave decomposition and applications to channel turbulence with streamwise rotation

Using helical-wave decomposition (HWD), a solenoidal vector field can be decomposed into helical modes with different wavenumbers and polarities. Here, we first review the general formulation of HWD in an arbitrary single-connected domain, along with some new development. We then apply the theory to a viscous incompressible turbulent channel flow with system rotation, including a derivation of helical bases for a channel domain. By these helical bases, we construct the inviscid inertial-wave (IW) solutions in a rotating channel and derive their existing condition. The condition determines the specific wavenumber and polarity of the IW. For a set of channel turbulent flows rotating about a streamwise axis, this channel-domain HWD is used to decompose the flow data obtained by direct numerical simulation. The numerical results indicate that the streamwise rotation induces a polarity-asymmetry and concentrates the fluctuating energy to particular helical modes. At large rotation rates, the energy spectra of opposite polarities exhibit different scaling laws. The nonlinear energy transfer between different helical modes is also discussed. Further investigation reveals that the IWs do exist when the streamwise rotation is strong enough, for which the theoretical predictions and numerical results are in perfect agreement in the core region. The wavenumber and polarity of the IW coincide with that of the most energetic helical modes in the energy spectra. The flow visualizations show that away from the channel walls, the small vortical structures are clustered to form very long columns, which move in the wall-parallel plane and serve as the carrier of the IW. These discoveries also help clarify certain puzzling problems raised in previous studies of streamwise-rotating channel turbulence.

Combined effects of flow curvature and rotation on uniformly sheared turbulence

This paper describes an experiment in which a uniformly sheared turbulence was subjected to simultaneous streamwise flow curvature and rotation about the streamwise axis. The distortion of the turbulence is complex but well defined and may serve as a test case for turbulence model development. The uniformly sheared turbulence was developed in a straight wind tunnel and then passed into a curved tunnel section. At the start of the curved section the plane of the mean shear was normal to the plane of curvature so as to create a three-dimensional or ‘out of plane’ curvature configuration. On entering the curved tunnel, the flow developed a streamwise mean vorticity that rotated the mean shear about the tunnel centreline through approximately 70°, so that the shear was nearly in the plane of curvature and oriented so as to have a stabilizing effect on the turbulence. Hot wire measurements of the mean velocity, mean vorticity, mean rate of strain and Reynolds stress anisotropy development along the wind tunnel centreline are reported. The observed effect of the mean shear rotation on the turbulence was to diminish the shear stress in the plane normal to the plane of curvature while generating non-zero values of the shear stress in the plane of curvature. A rotating frame was identified for which the measured mean velocity field took the form of a simple shear flow. The turbulence anisotropy was transformed to this frame to estimate the effects of frame rotation on the structure of sheared turbulence.

Turbulence Within a Turbomachine Rotor Wake Subject to Nonuniform Contraction

The flow and turbulence in a rotor near wake located within a nonuniform field, generated by a row of inlet guide vanes, are investigated experimentally in a refractive-index-matched facility that provides unobstructed view of the entire flowfield. Stereoscopic particle image velocimetry measurements, performed in closely spaced radial planes, enable measurements of all the components of the phase-averaged strain rate, Reynolds stress, and triple correlation tensors. The rotor wake is bent and compressed as a result of exposure to regions with high axial momentum (jets), which fill the gaps between inlet guide vanes wakes. As the rotor wake propagates away from the blade, this process of bending and compression by the jets leads to formation of distinct wake kinks containing regions of high turbulence (turbulent hot spots). We focus on an early stage of hot-spot formation. On the suction side of the wake, compression by a jet increases turbulence production, causing nonuniform and asymmetric distribution of Reynolds stresses. In a curvilinear coordinate system aligned with the wake centerline, all the Reynolds stresses are higher on the suction side of the wake where the decay rate of turbulence is much slower than that expected in wakes. The production rate of streamwise stress is dominated by interactions of the shear stress with the cross-stream gradients of the phase-averaged streamwise velocity. The latter also interact with the cross-stream stress to cause high production of shear stress, especially on the suction side. The locations of peak streamwise and shear stresses are consistent with those of the corresponding production rates. The similar locations of peak streamwise and cross-stream stresses, together with low production rate of the latter, suggest a significant contribution by intercomponent transfer from the streamwise to the cross-stream stress. The effects of streamwise curvature and rotation on the evolution of turbulent stresses are marginal. The paper also provides distributions of advection by phase-averaged flow and turbulent diffusion components. The diffusion terms oppose the peaks of production rates, but also have high values along the perimeter of the wake. We compare the distribution of diffusion of turbulent kinetic energy to a model based on the gradient-diffusion hypothesis. The model predicts the diffusion peak that opposes the production rate maximum quite well, but underpredicts the diffusion along the perimeter of the wake and overpredicts it near the wake center.

G1302 主流方向系回転一様剪断乱流の数値解析的研究(2)(GS13 数値シミュレーション,一般セッション)

Direct numerical simulation (DNS) for homogeneous turbulent shear flows in the streamwise system rotating is performed. In the turbulence energy, the streamwise rotation effect is smaller than the shear-direction and spanwise ones. In the budget of the Reynolds stress, the rotation term balances with the pressure strain one at the strong rotation case. The streamwise rotation effect has influence on the small-scale motion.

DNS of a Turbulent Channel Flow with Streamwise Rotation ‐ Study of the Reverse Effect of the Cross Flow

AbstractModeling of rotating turbulent flows is a major issue in engineering applications. In this work a turbulent channel flow rotating about the streamwise direction is presented. The theory is based on the investigations of [3] employing Lie group analysis. It was found that a cross flow in spanwise direction is induced. A series of direct numerical simulations (DNS) has been conducted for both different rotation rates and different Reynolds numbers to validate the cross flow. In addition some new interesting effects were observed. The averaged profile ū3 of the cross flow is formed like a ‘S’ that means it exhibits a triple zero‐crossing which denotes regions of reverse flow. Alaso a reverse effect is seen which means that for small rotation rates up to Ro=10 the spanwise mean velocity profiles increase and at rotation number Ro=14 this effect appears to reverse. Both effects were observed at two different Reynolds numbers Re = 180 and Re = 270. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)