Uniform Crossflow Research Articles

Vortex-induced vibration of a long flexible cylinder in uniform cross-flow

Numerical simulations are performed of a long flexible cylinder undergoing vortex-induced vibration at a Reynolds number of 500. The cylinder is pinned at both ends, having an aspect ratio of 100 (cylinder length to cylinder diameter) and a mass ratio of 4.2 (structural mass to displaced fluid mass). Temporal and spatial information on the cross-flow (CF) and in-line (IL) vibrations is extracted. High modal vibrations up to the 6th in the CF direction and the 11th in the IL direction are observed. Both the CF and IL vibrations feature a multi-mode mixed pattern. Mode competition is observed. The 2nd mode with a low frequency dominates the IL vibration and its existence is attributed to a wave group propagating back and forth along the span. Distributions of fluid force coefficients are correlated to those of the CF and IL vibrations along the span. Histograms of the x-y motion phase difference are evaluated from the total simulation time and a complete vibration cycle representing the standing or travelling wave pattern. Correlations between the phase difference and the vibrations are discussed. Vortex structures behind the cylinder show an interwoven near-wake pattern when the standing wave pattern dominates, but an oblique near-wake pattern when the travelling wave pattern prevails.

Nonlinear dynamics of three-dimensional vortex-induced vibration prediction model for a flexible fluid-conveying pipe

In this article, a three-dimensional nonlinear dynamic model, which takes into account both the geometric and hydrodynamic nonlinearities, is presented to characterize the behavior of a flexible fluid-conveying pipe under vortex-induced vibration by extended Hamilton's principle. It should be noted that the pipe conveying fluids is placed in a uniform cross flow. Two distributed and coupled van der Pol wake oscillators are utilized to model the fluctuating lift and drag coefficients, respectively. The finite element method is adopted to directly solve the highly coupled nonlinear fluid-structure interaction equations. Model validations are firstly performed through comparisons with published experimental data and numerical simulation results. The results show that the natural frequency will rapidly decrease with the increase of internal flow velocity. Parametric studies highlight that the maximum displacements and stresses of the riser can be increased or decreased depending on the internal flow velocity, and the critical internal flow velocities result in the increase of mode order for different cross-flow velocities. The opposite variation between axial and in-line or cross-flow displacement amplitude and maximum stress within the modal transition region is revealed. Moreover, the discontinuous jumping phenomenon of in-line response modal is discovered.

Nonlinear three-dimensional dynamics of a marine viscoelastic riser subjected to uniform flow

The three-dimensional nonlinear dynamic model of a long marine riser with Kelvin-Voigt viscoelasticity properties under vortex-induced vibration is proposed and investigated. The objective is to find the appropriate viscoelastic coefficients to suppress the nonlinear dynamic response of a marine riser. The pipe is placed in a uniform cross flow and geometric nonlinearities are considered. Two distributed and coupled Van der Pol wake oscillators are applied to characterize the fluctuating lift and drag coefficients, respectively. The highly nonlinear fluid-structure interaction equations are directly coupled and solved by the finite element method. Firstly, the model is validated by comparing with published experimental data and numerical simulation results. Then, modal analysis is performed to determine the impact of viscoelastic coefficients on the natural frequency for different damping values. A nonlinear dynamic analysis is carried out to determine the impacts of the viscoelastic coefficients on displacements, stresses, modal variation and phase portraits. The results show that the viscoelastic coefficients have a significant effect on the natural frequency of the studied marine riser. It is also demonstrated that appropriate viscoelastic coefficients are very important to effectively suppress the maximum displacements and stresses.

Locked-on vortex shedding modes from a rotationally oscillating circular cylinder

Numerical simulations of unsteady two-dimensional flow around a rotationally oscillating circular cylinder, placed in a uniform cross flow of a constant property Newtonian fluid, are performed at a fixed Reynolds number of 200. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using a higher order compact (HOC) formulation. The flow field is mainly influenced by Reynolds number, Re, maximum angular velocity of the cylinder, αm, and the frequency ratio, f/f0, which represents the ratio between the frequency of oscillation, f, and the natural vortex shedding frequency, f0. The ranges considered for these parameters are 0.5⩽αm⩽6.0 and 0.5⩽f/f0⩽3.0. The resulting vortex formation modes and lock-on phenomena behind the cylinder as well as the fluid forces acting on the cylinder are analyzed. Occurrence of new multiple lock-on regions is demonstrated in detail by the variation of f and αm. The instances of high drag reduction at high values of αm are confirmed. Comparisons with previous numerical and experimental results verify the accuracy and validity of the present study.

Experimental sensitivity of vortex-induced vibrations to localized wake perturbations

We present the experimental sensitivity of vortex-induced vibration (VIV) to localized perturbations, in the wake of a low mass-damping one-degree-of-freedom circular cylinder subject to uniform cross-flow. Regions of VIV sensitivity have been identified, clearly indicating positions in the wake where control systems should be placed in order to attenuate VIV amplitudes.As a validation of the sensitivity maps, we demonstrate how by using control cylinders with diameters of only 12% of the main cylinder diameter, reductions of VIV response of more than 65%, can be reached. The use of Digital Particle Image Velocimetry (DPIV) has allowed us to identify the physical mechanisms underlying the VIV response modifications induced by the control cylinders.

A new analytical scaling for turbulent wind-bent plumes: Comparison of scaling laws with analog experiments and a new database of eruptive conditions for predicting the height of volcanic plumes

Various scaling relationships relate the height of volcanic plumes to eruptive source conditions, atmospheric density stratification, turbulent entrainment, and wind stresses. However, observational, analog, and numerical studies used to test these scalings capture only a narrow range of natural eruptive conditions. In particular, existing analytical scalings are not appropriate for the wind stress conditions typical of the majority of volcanic eruptions. Accordingly, we develop a new analytical scaling for the height of buoyant plumes rising in density-stratified uniform crossflows. We compare this scaling to existing analytical scalings (Morton et al. 1956; Hewett et al. 1971) as well as “functional” scalings (i.e., parameterizations expressed as a function of the Morton et al. (1956) scaling and a regime parameter related to wind stress, Degruyter and Bonadonna (2012), Woodhouse et al. (2013), Carazzo et al. (2014)) using the extensive experimental dataset from Carazzo et al. (2014) along with natural events from a new database including 94 eruptive phases. Our proposed scaling best predicts the height of experimental plumes, which enables us to constrain the ratio of the wind to radial entrainment coefficients. For natural eruptions, the Woodhouse et al. (2013) and Carazzo et al. (2014) scalings, which account explicitly for wind gradient, best predicts plume heights. We show that accounting for atmospheric stratification and wind improves empirical relationships between mass eruption rates and plume heights. For tested scalings, analyze of residual heights for natural eruption supports the hypothesis that volcanic plumes rise higher in a wetter atmosphere. Finally, for analog plumes rising under moderate to high wind stresses, we show that plume shapes evolve over the plume height, violating the self-similarity assumption on which all scalings and integral model results rely. We discuss consequences for relaxing the self-similarity hypothesis as well as potential improvements for standard integral plume models, in turn.

Numerical simulation of flows past multiple cylinders using the hybrid Local Domain Free Discretization and Immersed Boundary Method

Study of the flow around a group of cylinders (such as risers of the offshore platforms) has been the challenging subject because of its inherent complexity. The research on this problem is important because flow interference between cylinders is responsible for some significant changes in the characteristics of fluid loads. In this paper, the hybrid Local Domain-Free Discretization-Immersed Boundary Method (LDFD-IBM), which combines the strengths of LDFD method and Immersed Boundary Method (IBM), is adopted to solve this problem. The advantages of the LDFD-IBM over conventional IBM are its truly second-order accuracy and simple implementation using a regular fixed Cartesian mesh. In the present investigation, the solver has been applied to simulate the unsteady viscous flow past two cylinders and three cylinders at different configurations in a uniform cross flow. The streamlines and vorticity contours are plotted for the flow visualization. The lift and drag coefficients time histories are presented.

Heat transfer from a heated non-rotating cylinder performing circular motion in a uniform stream

Forced convection from a heated non-rotating circular cylinder of radius a performing a circular motion of radius A∗ and placed in a uniform cross flow of constant properties fluid is investigated numerically. The two-dimensional governing equations of flow motion and energy are solved numerically using Fourier spectral analysis together with finite difference approximations to determine the flow field characteristics and the heat transfer parameters. The flow and thermal fields are mainly influenced by Reynolds numbers, Re, Prandtl number, Pr, amplitude of circular motion, Ar=A∗/a, and the frequency ratio, Fr=f∗/f0∗, which represents the ratio between the frequency of circular motion, f∗, and the natural vortex shedding frequency, f0∗. The ranges considered for these parameters are 60⩽Re⩽180, 0.1⩽Ar⩽1.0 and 0.5⩽Fr⩽3.0, while the Prandtl number is kept constant at 0.7. The study, in general, showed that the heat transfer rate increases appreciably in the high range of Re, Ar and Fr. Comparisons with previous numerical and experimental results verify the accuracy and the validity of the present study.

Laminar boundary layers with uniform shear cross flow

Laminar boundary layers with fully developed uniform shear cross flows are considered. The first streamwise laminar flow is a Blasius boundary layer flow, the second is uniform shear flow over a semi-infinite plate, and the third is the flow induced by a power-law stretching surface. In the first two cases, the effect of streamwise plate motion is taken into account by the parameter λ. In each case, the similarity solutions reduce the governing boundary layer equations to a primary ordinary differential equation for the streamwise flow and a secondary linear equation coupled to the primary solution for the cross flow. It is found that an infinity of solutions exist in each problem and the unique solution in each case is found by applying the Glauert criterion. In some instances, a simple exact solution for the cross flow is presented. Results for the wall shear stresses and velocity profiles are given in graphical form.

Influence of hydrodynamic slip on convective transport in flow past a circular cylinder

The presence of a finite tangential velocity on a hydrodynamically slipping surface is known to reduce vorticity production in bluff body flows substantially while at the same time enhancing its convection downstream and into the wake. Here, we investigate the effect of hydrodynamic slippage on the convective heat transfer (scalar transport) from a heated isothermal circular cylinder placed in a uniform cross-flow of an incompressible fluid through analytical and simulation techniques. At low Reynolds (Re > 1) numbers, our theoretical analysis based on Oseen and thermal boundary layer equations allows for an explicit determination of the dependence of the thermal transport on the non-dimensional slip length l(s). In this case, the surface-averaged Nusselt number, Nu transitions gradually between the asymptotic limits of Nu similar to Pe(1/3) and Nu similar to Pe(1/2) for no-slip (l(s) -> 0) and shear-free (l(s) -> infinity) boundaries, respectively. Boundary layer analysis also shows that the scaling Nu similar to Pe(1/2) holds for a shear-free cylinder surface in the asymptotic limit of Re >> 1 so that the corresponding heat transfer rate becomes independent of the fluid viscosity. At finite Re, results from our two-dimensional simulations confirm the scaling Nu similar to Pe(1/2) for a shear-free boundary over the range 0.1 <= Re <= 10(3) and 0.1 <= Pr <= 10. A gradual transition from the lower asymptotic limit corresponding to a no-slip surface, to the upper limit for a shear-free boundary, with l(s), is observed in both the maximum slip velocity and the Nu. The local time-averaged Nusselt number Nu(theta) for a shear-free surface exceeds the one for a no-slip surface all along the cylinder boundary except over the downstream portion where unsteady separation and flow reversal lead to an appreciable rise in the local heat transfer rates, especially at high Re and Pr. At a Reynolds number of 10(3), the formation of secondary recirculating eddy pairs results in appearance of additional local maxima in Nu(theta) at locations that are in close proximity to the mean secondary stagnation points. As a consequence, Nu exhibits a non-monotonic variationwith l(s) increasing initially from its lowermost value for a no-slip surface and then decreasing before rising gradually toward the upper asymptotic limit for a shear-free cylinder. A non-monotonic dependence of the spanwise-averaged Nu on l(s) is observed in three dimensions as well with the three-dimensional wake instabilities that appear at sufficiently low l(s), strongly influencing the convective thermal transport from the cylinder. The analogy between heat transfer and single-component mass transfer implies that our results can directly be applied to determine the dependency of convective mass transfer of a single solute on hydrodynamic slip length in similar configurations through straightforward replacement of Nu and Pr with Sherwood and Schmidt numbers, respectively.

Vortex-induced rotations of a rigid square cylinder at low Reynolds numbers

A numerical investigation of vortex-induced rotations (VIRs) of a rigid square cylinder, which is free to rotate in the azimuthal direction in a two-dimensional uniform cross-flow, is presented. Two-dimensional simulations are performed in a range of Reynolds numbers between 45 and 150 with a fixed mass and moment of inertia of the cylinder. The parametric investigation reveals six different dynamic responses of the square cylinder (expanding on those reported by Zaki et al. (J. Fluids Struct., vol. 8, 1994, pp. 555–582)) and their coupled vortex patterns at low Reynolds numbers. In each characteristic regime, moment generating mechanisms are elucidated with investigations of instantaneous flow fields and surface pressure distributions at chosen time instants in a period of rotation response. Our simulation results also elucidate that VIRs significantly influence the statistics of drag and lift force coefficients: (i) the onset of a rapid increases of the two coefficients at $Re=80$ and (ii) their step increases in the autorotation regime.

Effect of the nature of vitiated crossflow on the flow-field of a transverse reacting jet

The effect of the nature of vitiated crossflow on the structure and dynamics of non-reacting/reacting transverse jets is investigated. In this study, the vitiated crossflow is produced either by a low-swirl burner (LSB) that adds a swirling component to the crossflow or a bluff-body burner (BBB) that produces a uniform crossflow. The jet fluid is injected through a contoured injector, which provides a top-hat velocity profile. The swirling crossflow exhibits considerable swirl at the point of injection of the transverse jet. Two component high-repetition-rate PIV measurements demonstrate the influence of a vitiated crossflow generated by a low-swirl/bluff-body burner on the near-wake flow-field of the jet. Measurements at a plane below the injection location of the jet indicate that there is a continuous entrainment of PIV particles in case of swirling crossflow. The time-averaged flow-field shows that the velocity field for reacting/non-reacting jets in the LSB crossflow exhibits higher velocity gradients, in the measurement plane along jet cross section, as compared to BBB crossflow. It is found that the vorticity magnitude is lower in case of jets in the BBB crossflow and there is a delay in the formation of the wake vortex structure. The conditional turbulent statistics of the jet flow-field in the two crossflows shows that there is a higher degree of intermittency related to the wake vortex structure in case of a BBB crossflow, which results in a non-Gaussian distribution of the turbulent statistics. The wake Strouhal number calculation shows the influence of the nature of crossflow on the rate of wake vortex shedding. The wake Strouhal number for the jets in BBB crossflow is found to be lower than for the LSB crossflow. A decrease in the wake Strouhal number is observed with an increase in the nozzle separation distance. There is an increase in the dilatation rate owing to heat release which results in higher wake Strouhal number for reacting jets as compared to non-reacting jets. The POD analysis of the reacting and non-reacting jets shows the wake vortex structures to be the dominant flow structures in this study. There is a redistribution of turbulent kinetic energy from the shear layer to the coherent wake vortex structure with an increase in the nozzle separation distance. The wake structures in the near-wake region of jets in LSB crossflow are found to have a larger contribution to the kinetic energy as compared to jets in BBB crossflow.

Nonlinear dynamics of a fluid-conveying pipe under the combined action of cross-flow and top-end excitations

We report a theoretical investigation of an elastic and slender fluid-conveying pipe with a top-end excitation subjected to uniform cross flows. Considering the mean drag force and the time varying vortex-induced lift force which is modeled using a nonlinear van der Pol oscillator, the nonlinear partial differential equations of the motion of coupled fluid-structure system are constructed and simplified to a reduced-order model through the Galerkin-type discretization. By virtue of quasi-static displacement conditions, the characteristics of vortex-induced vibration of the pipe are evaluated for the first two lock-in modes. The results show that the top-end excitation can increase the vibration amplitude of the pipe when the cross-flow speed is out of the lock-in regions. When the cross-flow speed is within the lock-in region, however, the top-end oscillation causes a transition between quasi-periodic and periodic in the responses of the pipe, significantly reducing or increasing the vibration amplitudes depending on the excitation acceleration and frequency. This finding has an important guidance in suppressing vortex-induced vibrations by balancing the internal fluid velocity and the top-end excitation.

Film cooling effectiveness enhancement using surface dielectric barrier discharge plasma actuator

The case presented here deals with the enhancement of film cooling effectiveness using plasma flow control. In this experimental study, a jet is injected from an elongated slot into a thermally uniform cross-flow. The influence of a surface plasma dielectric barrier discharge actuator on heat transfer downstream of the slot is investigated. 2D PIV and IR-thermography measurements are performed for three different blowing ratios of M = 0.4, 0.5 and 1. Results show that the effectiveness can be increased when the discharge is switched-on. Whatever the blowing ratio, the actuator induces a deflection of the jet flow towards the wall, increases its momentum and delays its diffusion in the cross-flow. The best results are obtained with a blowing ratio close to 0.5 and an steady actuation without any frequency modulation.

Flow control of an elongated jet in cross-flow: Film cooling effectiveness enhancement using surface dielectric barrier discharge plasma actuator

The case presented here deals with plasma flow control applied to a cross-flow configuration, more specifically to a film cooling system. The ability of a plasma dielectric barrier discharge actuator for film cooling effectiveness enhancement is investigated through an experimental set-up, including a film injection from an elongated slot into a thermally uniform cross-flow. Two-dimensional particle image velocimetry and infrared-thermography measurements are performed for three different blowing ratios of M = 0.4, 0.5, and 1. Results show that the effectiveness can be increased when the discharge is switched on, as predicted by the numerical results available in literature. Whatever the blowing ratio, the actuator induces a deflection of the jet flow towards the wall, increases its momentum, and delays its diffusion in the cross-flow.

Flow-induced vibrations of in-line cylinder arrangements at low Reynolds numbers

The present study numerically explores the limiting two degrees of freedom (streamwise and transverse) free oscillation response of three circular cylinders, placed in an in-line configuration subjected to a uniform cross flow at low Reynolds numbers. Three identical cylinders with a low mass ratio (m⁎=4/π) and zero damping are considered. The spacing between the cylinders L/D is equal to 4. The reduced velocity Ur is varied from 2 to 13 for two values of the Reynolds number (Re=100 and Re=150). For comparison purposes, the free oscillation responses of an isolated cylinder and a tandem cylinder pair under the same conditions are also evaluated. The results show that the dynamic behaviors of three in-line cylinders are significantly different from those of the tandem cylinder pair. While the maximum transverse oscillation amplitude increases by about 25%, there is now a very large streamwise oscillation amplitude (AX/D≈1.3), comparable to those in the transverse direction. They appear at Ur>9. The frequency responses of the triple cylinder case are much richer; in particular, at higher Ur. There is a clear low frequency component which is most evident in the streamwise direction. Many of the displacement trajectories of the triple cylinder case can almost be described as “bounded random movements”. The associated phase portraits and the Poincaré maps show that the dynamical characteristics of the triple cylinder configuration are considerably richer than those of the tandem cylinder pair. Even at such low Re, the free oscillations of three in-line cylinders already seem to approach a chaotic response. In particular, there is evidence that the fluid–structure system approaches to chaos via the quasi-periodic route. Due to such much more complex dynamical characteristics, it is therefore highly risky to predict the free oscillation behaviors of multiple in-line cylinders by extrapolating those of the tandem cylinder pair.

A Review on Empirical Correlations for Jet/Spray Trajectory of Liquid Jet in Uniform Cross Flow

The empirical correlations for the prediction of jet/spray penetration of liquid jet in subsonic uniform crossflow are reviewed in this study. Considerable number of empirical correlations had been proposed by many investigators. It has generally known that the jet/spray trajectory of a liquid jet in a cross-flow is a function of the liquid to air momentum flux ratio and the normalized distance in the airstream direction from the injector. However, several researchers incorporated the Weber number, liquid-to-water or air viscosity ratio, pressure ratio or Reynolds number, temperature ratio in the empirical correlations. Two different classification methods of correlations, i.e. classification based on mathematic functional form and classification based on flow regime, are introduced in this study. The one classification of existing correlations based on functional form includes correlations in a power-law, logarithmic, and exponential forms, respectively. The other classification of previous correlations based on flow regime includes one, two and three regime, correlations. Correlations in a power-law functional form can be further divided into three groups such as momentum flux ratio, Weber number and other parameters forms. Correlations in logarithmic functional form can be also grouped as momentum flux ratio and Weber number forms. Most of the evaluation studies reported the significant discrepancies of predicted values by the existing correlations. The possible reasons for discrepancies will be summarized as measurement technique, assumptions made in defining terms in the liquid to air momentum flux ratio, difficulties in defining the boundaries of the liquid jets, turbulence level in the core and boundary layer of incoming jet and gas flows, nozzle/injector geometry and its position in the crossflow. However, it can be found from the several evaluation studies that the power-law functional form with momentum flux ratio and two regimes correlations provided relatively the best fit to experimental data.

The stability of the heated plane Poiseuille flow subjected to a uniform crossflow

The Poiseuille flow of an incompressible viscous fluid confined between two parallel porous horizontal walls, and subjected to an adverse temperature gradient, is studied numerically. A uniform crossflow is considered across the fluid layer. The crossflow modifies the velocity field and the temperature field in the basic state which affects the onset of the instability. The stability of the basic state is discussed with respect to the Rayleigh number at the fixed small values of the Reynolds number and with respect to the Reynolds number at the fixed values of the Rayleigh number. The crossflow is found to stabilize or destabilize the basic state, depending upon its magnitude and direction. The onset of instability also depends upon the Prandtl number of the fluid.

A Model for Temperature Fluctuations in a Buoyant Plume

We present a hybrid Lagrangian stochastic model for buoyant plume rise from an isolated source that includes the effects of temperature fluctuations. The model is based on that of Webster and Thomson (Atmos Environ 36:5031–5042, 2002) in that it is a coupling of a classical plume model in a crossflow with stochastic differential equations for the vertical velocity and temperature (which are themselves coupled). The novelty lies in the addition of the latter stochastic differential equation. Parametrizations of the plume turbulence are presented that are used as inputs to the model. The root-mean-square temperature is assumed to be proportional to the difference between the centreline temperature of the plume and the ambient temperature. The constant of proportionality is tuned by comparison with equivalent statistics from large-eddy simulations (LES) of buoyant plumes in a uniform crossflow and linear stratification. We compare plume trajectories for a wide range of crossflow velocities and find that the model generally compares well with the equivalent LES results particularly when added mass is included in the model. The exception occurs when the crossflow velocity component becomes very small. Comparison of the scalar concentration, both in terms of the height of the maximum concentration and its vertical spread, shows similar behaviour. The model is extended to allow for realistic profiles of ambient wind and temperature and the results are compared with LES of the plume that emanated from the explosion and fire at the Buncefield oil depot in 2005.

Convective Transport Around Rows of Square Cylinders Arranged in a Staggered Fashion at Moderate Reynolds Number

The thermohydrodynamic interactions among multiple bodies fixed in an incident flow are analyzed through two-dimensional numerical computation. The bodies are identical in shape and size with square cross section and arranged in two rows in a staggered fashion within an unconfined domain. Simulation is carried out using a finite-volume-based method considering a uniform cross flow of air (Prandtl number, Pr =0.71) at a moderate Reynolds number (Re = 100). Apart from the Reynolds number, certain geometrical parameters such as the streamwise and transverse spacing of the objects may significantly influence the wake dynamics, vortex structure formation, and the associated thermal transport. Accordingly, both the dimensionless transverse spacing (S/d = 1, 3, and 5, with S and d the transverse spacing and cylinder size, respectively) and the nondimensional streamwise gap (L/d = 1, 3, and 5, with L being the streamwise gap) are varied to elucidate their roles in controlling the hydrodynamic and thermal transport. Even at such a moderate Reynolds number, the flow and thermal fields show chaotic behavior at smaller transverse spacing, this behavior being established through various chaos characterization tools. However, at larger spacing, the usual unsteady vortex dynamics persists. Shedding in the gap is inhibited at smaller streamwise spacing. Again, at larger spacing, the normal shedding characteristics continue. Average heat transfer from the cylinders is higher at smaller streamwise and transverse spacing.