Mechanism of drag reduction by spanwise oscillating Lorentz force in turbulent channel flow

Numerical simulations and experimental research are both carried out to investigate the controlled effect of spanwise oscillating Lorentz force on a turbulent channel flow. The variations of the streaks and the skin friction drag are obtained through the PIV system and the drag measurement system, respectively. The flow field in the near-wall region is shown through direct numerical simulations utilizing spectral method. The experimental results are consistent with the numerical simulation results qualitatively, and both the results indicate that the streaks are tilted into the spanwise direction and the drag reduction utilizing spanwise oscillating Lorentz forces can be realized. The numerical simulation results reveal more detail of the drag reduction mechanism which can be explained, since the spanwise vorticity generated from the interaction between the induced Stokes layer and intrinsic turbulent flow in the near-wall region can make the longitudinal vortices tilt and oscillate, and leads to turbulence suppression and drag reduction.     

Evolution of global enstrophy in cylinder wake controlled by Lorentz force

The Okubo-Weiss function is correlated with the fluid particle compression, deformation and vorticity, which provides a simple way to characterize different regions of a flow-field. In the present paper, it shows mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries. To validate the conclusion, a flow passing a circular cylinder con- trolled by the electromagnetic force is calculated numerically as an example. Distributions of global enstrophy, total squared strain and Okubo-Weiss function in the controlled flow field are discussed. The influence of Lorentz force on the distribution is analyzed.     

Influences of Lorentz force on the hydrofoil lift

In this paper, Lorentz forces are proved to be able to suppress separation in flows over hydrofoils. Furthermore, a differential equation of pressure distributions on the hydrofoil surface is derived, from which it is found that BVF （boundary vortex flux） σ is a suitable criterion for describing the lift coefficient variations during the electromagnetic control process. According to our numerical results, the periodic variations of lift for a hydrofoil at an attack angle of 17 ° are analyzed and its inherent mechanism is discussed in detail with the concept of BVE On the other hand, the effects of Lorentz force on the hydrofoil＇s lift are investigated both experimentally and numerically for different magnitudes and locations.     

Flow behavior around a square cylinder subject to modulation of a planar jet issued from upstream surface

The flow behavior in the up- and downstream regions of a square cylinder subject to the modulation of a planar jet issued from the cylinder׳s front surface was studied using the laser-assisted smoke flow visualization method and hot-wire anemometer measurement. Reynolds numbers were from 1628 to 13 000. The drag force experienced by the square cylinder was obtained by measuring the surface pressures on the up- and downstream faces. The temporally evolving smoke flow patterns in the up- and downstream regions were synchronously revealed through the smoke flow visualization. The frequency characteristics of the instability waves in the up- and downstream regions were synchronously detected by the two hot-wire anemometers. Four characteristic flow modes were observed within the different ranges of the injection ratios. At the low injection ratios (IR<1), the ‘swinging jet’ appeared. The jet swung periodically leftward and rightward and formed a fluid bubble on the front surface. The fluid bubble contained a pair of counter-rotating vortices and presented a periodic variation in its height. At moderately low injection ratios (1<IR<4.3), the ‘deflected oscillating jet’ appeared. The jet was deflected in either the left or the right direction and wrapped around one of the edges of the square cylinder. Both the swinging and oscillating motions of the jet in the swinging jet and deflected oscillating jet modes were induced by the periodic feedback pressure signals generated by the vortex shedding in the wake. At the moderately high (4.3<IR<8.3) and high (IR>8.3) injection ratios, the ‘deflection jet’ and ‘penetrating jet’ appeared. The jet detached from the cylinder׳s front surface and penetrated a long distance into the upstream region due to large jet momentum. Neither periodic jet oscillation in the upstream region nor vortex shedding in the wake was observed. The drag coefficient was found to be decreasing quickly with increasing the injection ratio.     

Flow structure of wake behind a rotationally oscillating circular cylinder

Flow around a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally. The dominant parameters affecting this experiment are the Reynolds number (Re), oscillation amplitude (θ_A), and frequency ratio F_R=f_f/f_n, where f_f is the forcing frequency and f_n is the natural frequency of vortex shedding. Experiments were carried out under conditions of Re=4.14×10³, 0°θ_A60° and 0.0F_R2.0. Rotational oscillation of the cylinder significantly modified the flow structure in the near-wake. Depending on the frequency ratio F_R, the cylinder wake showed five different flow regimes, each with a distinct wake structure. The vortex formation length and the vortex shedding frequency were greatly changed before and after the lock-on regime where vortices shed at the same frequency as the forcing frequency. The lock-on phenomenon always occurred at F_R=1.0 and the frequency range of the lock-on regime expanded with increasing oscillation amplitude θ_A. In addition, the drag coefficient was reduced when the frequency ratio F_R was less than 1.0 (F_R<1.0) while fixing the oscillation amplitude at θ_A=30°. When the oscillation amplitude θ_A was used as a control parameter at a fixed frequency ratio F_R=1.0 (lock-on regime), the drag reduction effect was observed at all oscillation amplitudes except for the case of θ_A=30°. This type of active flow control method can be used effectively in aerodynamic applications while optimizing the forcing parameters.     

Measurement of instantaneous velocity and surface topography in the wake of a cylinder at low Reynolds number

A technique capable of simultaneous measurement of free-surface topography and velocity vector field data is presented. This technique offers substantial benefits of both reduced complexity and enhanced accuracy over all other techniques known to offer the same measurements. The flow behind a circular cylinder at low Reynolds numbers is measured using this technique. The velocity and vorticity fields as well as Strouhal number closely match the expected results. The free-surface topography, which can be related to the pressure field, exhibits an intimate relationship to the vorticity field.     

The effect of modeled drag reduction on the wall region

The low-dimensional model derived for the wall region of a turbulent boundary layer (Aubry et al., 1988) is applied to a drag-reduced flow. In agreement with some experimental results, drag reduction is modeled by thickening the wall region, which is achieved by applying stretching transformations to the original flow. By application of a Galerkin projection, a set of ordinary differential equations (ODEs) is obtained whose structure is identical to the set corresponding to the unmodified flow. The coefficients of the ODEs are modified in a nontrivial way. The bifurcation diagrams plotted for different values of the stretching parameter are different in detail but the structure is globally the same. In particular, the intermittent behavior which Aubry et al. identified with the cyclic bursting events experimentally observed is still present. The scenario by which intermittency appears through a subcritical Hopf bifurcation in which a heteroclinic cycle is created and disappears through a bifurcation to traveling waves is identical. These results hold for values of the stretching between 1 and 2.65, the value at which the top of the buffer layer reaches the centerline of the pipe. This is in agreement with experimental results for flows whose drag is reduced but which still display intermittency. The bifurcations occur in the stretched flow at increased levels of dissipation (relative to the unstretched flow), consistent with theoretical pictures of drag reduction, in which the increase of scale is due to stabilization by an increase of dissipation in the turbulent part of the flow. Moreover, this method is a systematic way to perturb the coefficients of the ODEs of Aubry et al. (1988). Under this kind of perturbation, the behavior of the solution (in the part of the bifurcation diagram physically relevant) is found to be extremely robust.     

Numerical study of the suppression mechanism of vortex-induced vibration by symmetric Lorentz forces

In this paper, the electro-magnetic control of vortex-induced vibration (VIV) of a circular cylinder is investigated numerically based on the stream function–vorticity equations in the exponential–polar coordinates attached on the moving cylinder for Re=150. The effects of the instantaneous wake geometries and the corresponding cylinder motion on the hydrodynamic forces for one entire period of vortex shedding are discussed using a drag–lift phase diagram. The drag–lift diagram is composed of the upper and lower closed curves due to the contributions of the vortex shedding but is magnified, translated and turned under the action of the cylinder motion. The Lorentz force for controlling the vibration cylinder is classified into the field Lorentz force and the wall Lorentz force. The symmetric field Lorentz force will symmetrize the flow passing over the cylinder and decreases the lift oscillation, which, in turn, suppresses the VIV, whereas the wall Lorentz force has no effect on the lift. The cylinder vibration increases as the work performed by the lift dominates the energy transfer. Otherwise, the cylinder vibration decreases. If the net transferred energy per motion is equal to zero, the cylinder will vibrate steadily or be fixed.     

Critical effects of a spanwise surface wire on flow past a circular cylinder and the significance of the wire size and Reynolds number

An experimental study is conducted on flow past a circular cylinder fitted with a single spanwise wire on its surface. The work investigates the dependency of the critical wire locations on the wire size and Reynolds number, and examines the near wake and vortex shedding characteristics in an effort to advance the understanding of the critical wire effects beyond the existing literature. The Reynolds number is varied from 5000 to 30 000, and the wire diameter is varied from 2.9% to 5.9% of the cylinder diameter. All wires are larger than the boundary-layer thickness forming around a comparable smooth cylinder. Constant Temperature Anemometry and hydrogen bubble visualization are used as the flow diagnostic tools. The frequency and strength of the Karman instability are shown to vary with the wire location at any given Reynolds number nearly in an inverse fashion. For all the Reynolds numbers and wire sizes considered, two types of critical locations are shown to exist on the cylinder surface for the application of a wire. These locations are associated with the attenuation and amplification of the Karman instability, and in accord with the existing literature, are denoted as θ_c1 and θ_c2, respectively. The present work reveals that θ_c2 consists of a wide range of locations which remains unaffected from the wire size and Reynolds number, while θ_c1 is a relatively distinct location on the cylinder surface and depends on both the Reynolds number and wire size. For a given Reynolds number, increasing the wire size decreases θ_c1. For a given wire size, increasing the Reynolds number from 5000 to 15 000 increases θ_c1, and past 15 000, θ_c1 remains unaffected from the Reynolds number. When a wire is at θ_c1, even though, for the majority of the time the regular formation of Karman vortices ceases, the present data also reveals intermittent, short time periods where the regular shedding resumes.     

The influence of polyvinylacetate additive in water on turbulent velocity field and drag reduction

The effect of polymer concentration on drag reduction was studied experimentally with diluted water solutions of polyvinylacetate in a 2.4 cm I. D. pipe. The instantaneous local velocities of the velocity fields were measured by a one-channel differential laser-Doppler anemometer DISA Mark II, with forward scattering. Concentrations of water-polyvinylacetate over the range from 10 to 2,000 ppm were used. The drag reduction coefficient is proportional to the concentration and hydrolysis degree of the saponificated polyvinylacetate (PVAC) employed. A mechanical degradation in the turbulent shear flow was not observed.List of Symbols a ₁ coefficient in Eq. (3) - a ₂ coefficient in Eq. (3) - D pipe diameter - k coefficient in modified Blasius equation for friction factor - K consistency parameter given by (1 b) - K _i coefficients in Eq. (5) - m coefficient in Eq. (3) - n flow index Eq. (1a), coefficient in Eq. (3) - n ⁺ dimensionless position parameter defined by Eq. (4) - N ⁺ position parameter defined by Eq. (7) - r radial distance from the pipe center - R pipe radius - Re Reynolds number - Re _g generalized Reynolds number, Eq. (9) - t temperature - u ⁺ dimensionless local velocity, /u ^* - u ^* dynamic friction velocity, w(/8) ^0,5 - U ⁺ dimensionless local mean velocity defined by Eq. (6) - time-averaged local velocity - _m time-averaged local velocity at the pipe center - w average velocity over the cross-section of the pipe - X concentration of polymer in water, w · ppm - y distance from the pipe wall - y ⁺ dimensionless distance from the pipe wall, y u ^* / or as in Eq. (8) - friction factor in drag reduction flow - ₀ friction factor of pure water - degree of drag reduction - viscosity - standard deviation A version of this paper was presented at the 9th National Symposium on the measurement of turbulence with laser Doppler and other anemometers, Bratislava, CSSR, 1986     

Numerical study on the suppression of the vortex-induced vibration of an elastically mounted cylinder by a traveling wave wall

In the present paper, the commercial CFD code “Fluent” was employed to perform 2-D simulations of an entire process that included the flow around a fixed circular cylinder, the oscillating cylinder (vortex-induced vibration, VIV) and the oscillating cylinder subjected to shape control by a traveling wave wall (TWW) method. The study mainly focused on using the TWW control method to suppress the VIV of an elastically supported circular cylinder with two degrees of freedom at a low Reynolds number of 200. The cross flow (CF) and the inline flow (IL) displacements, the centroid motion trajectories and the lift and drag forces of the cylinder that changed with the frequency ratios were analyzed in detail. The results indicate that a series of small-scale vortices will be formed in the troughs of the traveling wave located on the rear part of the circular cylinder; these vortices can effectively control the flow separation from the cylinder surface, eliminate the oscillating wake and suppress the VIV of the cylinder. A TWW starting at the initial time or at some time halfway through the time interval can significantly suppress the CF and IL vibrations of the cylinder and can remarkably decrease the fluctuations of the lift coefficients and the average values of the drag coefficients; however, it will simultaneously dramatically increase the fluctuations of the drag coefficients.     

The influence of the injection system on drag reduction

The influence of the injection system for centerline injected polymer solutions (threads) on drag reduction in a turbulent pipe flow was studied using injectors of different length and grids. Compared with a short injector, the long injector showed a different behavior: the drag reduction was lower and its onset point was shifted to higher Reynolds numbers.The velocity profiles for the polymer-phase and the water-phase were measured simultaneously with a combination of laser-Doppler-velocimetry LDV and laser-induced fluorescence LIE It was found that the analysis of the LDV measurements with respect to the difference in velocity between the polymer-phase and the water-phase can give information about the mixing between both phases. For a Reynolds number of 30000 the difference between the phases is comparatively large for low drag reduction and very small for high drag reduction. The results indicate that the drag reduction achieved by injecting a concentrated polymer solution is mainly caused by a mixing process between polymer and water.     

Features of the turbulent wall pressure field on a long towed cylinder

Turbulent wall pressure fluctuation correlation functions were measured in water on a towed cylindrical model of length 129.8 m and diameter 3.8 cm for steady speeds ranging from 6.2 to 15.5 m/s. The drag on the model was measured with a strut-mounted load cell to provide estimates of the momentum thickness and friction velocity that are used for scaling the correlation functions. Very high momentum thickness Reynolds numbers Re_θ were achieved, and varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of boundary layer thickness to cylinder radius was approximately 24, which is an order of magnitude greater than previous laboratory investigations. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re_θ. A similarity scaling is shown to be more effective than outer or inner boundary layer scalings for collapsing the correlation functions. Comparisons with the early streamwise and transverse correlation measurements of Willmarth and Yang are favorable, and show consistent trends of a more rapid loss of correlated energy for cylindrical turbulent boundary layers than for flat plate cases. Convection velocities are also presented and shown to collapse well with separation scaled on outer variables. A simple model that relates the peak of the correlation function to the average coherence levels is shown to be valid for spatial separations less than the approximate momentum thickness.     

VIV suppression of a two-degree-of-freedom circular cylinder and drag reduction of a fixed circular cylinder by the use of helical grooves

Experimental investigations have been carried out to examine the effects of triple-starting helical grooves on the drag of fixed circular cylinders and the vortex-induced vibration of elastically supported cylinders. For the elastically supported cylinder, the Reynolds number varied from 1.3×10⁴ to 4.6×10⁴, whilst for the fixed cylinder from 3.1×10⁴ to 3.75×10⁵. A comparative approach which allows direct comparisons of the results was adopted where two cylinders of identical dimensions and physical properties with or without helical surface grooves were tested in exactly same experimental set-ups. In the elastically supported cylinder tests, the cylinders were attached to a vertically cantilevered supporting rod and towed in a towing tank. Both the in-line and cross-flow vibrations were permitted. In the fixed cylinder tests, the cylinders were supported on rigid vertical struts and towed horizontally in the same towing tank. It is found that for the case investigated the helical grooves were effective in suppressing the vortex-induced cross-flow vibration amplitudes with the peak amplitude reduced by 64%. Drag reductions of up to 25% were also achieved in the sub-critical Reynolds number range tested in the study for the fixed cylinders.     

The oseen flow of finite clusters of spheres and the wake effect on the drag factor

In this paper, the wake effect on drag factor in the axisymmetric Oseen flow of the finite clusters of equally spaced spheres with same size is studied. Putting the Oseen lets on the centres of all the spheres, the series solution of the problem is obtained. By truncating the infinite series and applying the collocation method to solve a set of the linear algebraic equations, the approximate solution of the Oseen flow of finite clusters of spheres and the drag factor for each sphere are presented. The effect of the sphere number and spacing on the drag factor of each sphere under different Reynolds numbers are calculated and the wake effect as well as the shielding effect and the end effect are revealed. The influence of various parameters on the effects is considered and compared with the corresponding results of the Stokes flow. The convergence of the method is also studied numerically in this paper.     

Measurements of the dynamic lift force acting on a circular cylinder in cross-flow and exposed to acoustic resonance

A piezoelectric transducer is developed to perform direct measurements of the dynamic lift force acting on a circular cylinder in cross-flow, in the presence and absence of acoustic resonance. Details of the force transducer design are presented in the paper. The dynamic lift force is measured for a single cylinder with two different diameters, D=12.7 and 15.8 mm. During the tests, the first transverse acoustic mode of the duct housing the cylinder is self-excited. The fluctuating pressure on the top wall of the duct is measured simultaneously with the dynamic lift force. In the absence of acoustic resonance, the measured dynamic lift coefficients agree favorably with those reported in the literature. However, when the acoustic resonance is initiated, the dynamic lift experiences a drastic increase in amplitude associated with abrupt changes in the phase between the lift force and the acoustic pressure. A methodology to extract the hydrodynamic lift component from the total lift measured during acoustic resonance is also proposed. The hydrodynamic lift force is then decomposed into in-phase and out-of-phase components, with respect to the resonant sound pressure. This decomposition procedure provides new insights into the nature of the aeroacoustic sources in the cylinder wake. The proposed methodology, together with the test results provide a general design approach to assess the increase in the dynamic fluid loading on bluff bodies in cross-flow due to the excitation of acoustic resonance.     

The effect of an unsteady drag force on the structure of a non-equilibrium region behind a shock wave in a gas-particle mixture

For numerical analysis of shock wave propagation in gas-particle mixtures, drag coefficients of a sphere in steady flows are generally used. However, it is shown both experimentally and numerically that a shock loaded solid sphere experiences unsteady drag forces. The paper describes a model of unsteady drag force and its effect on the structure of the non-equilibrium region behind a shock front traveling in a dusty gas. The results are compared with those obtained by using a steady drag coefficient and are discussed. It is demonstrated that the large drag force at the early stage of the interaction between shock-wave induced flow and a solid particle affects the flow structure that is obtained with a steady drag force.      

The effect of air-water interface on the vortex shedding from a vertical circular cylinder

The flow past an interface piercing circular cylinder at the Reynolds number Re=2.7×10⁴ and the Froude numbers Fr=0.2 and 0.8 is investigated using large-eddy simulation. A Lagrangian dynamic subgrid-scale model and a level set based sharp interface method are used for the spatially filtered turbulence closure and the air-water interface treatment, respectively. The mean interface elevation and the rms of interface fluctuations from the simulation are in excellent agreement with the available experimental data. The organized periodic vortex shedding observed in the deep flow is attenuated and replaced by small-scale vortices at the interface. The streamwise vorticity and the outward transverse velocity generated near the edge of the separated region, which enforces the separated shear layers to deviate from each other and restrains their interaction, are primarily responsible for the devitalization of the periodic vortex shedding at the interface. The lateral gradient of the difference between the vertical and transverse Reynolds normal stresses, increasing with the Froude number, is the main source of the streamwise vorticity and the outward transverse velocity at the interface.