Volume 27, Issue 7, July 2015
Index of content:
 LETTERS


Velocity derivative skewness in fractalgenerated, nonequilibrium grid turbulence
View Description Hide DescriptionThe evolution of the velocity derivative skewness, S(∂u/∂x), is investigated along two streamwise axes and four transverse positions in the wake of a squarefractalelement grid. In the nearfield, the produced turbulence exhibits nonequilibrium characteristics including . In the farfield, the turbulence agrees with canonical grid turbulence results and C ϵ is approximately constant. It is found that in the nonequilibrium region, the value of −S(∂u/∂x) is dependent on both streamwise and transverse positions, but after a sufficient decay period, it takes on a near constant value in the farfield. It is demonstrated that the evolution C ϵ approximately corresponds to that of −S(∂u/∂x), which is suggestive that some of the nonequilibrium properties are likely a result of residual strain from the turbulence generating conditions.

 ARTICLES

 Interfacial Flows

Wave drag on a submerged sphere
View Description Hide DescriptionWe measure the wave drag acting on fully submerged spheres as a function of their depth and velocity, with an apparatus that measures only the component of the drag due to the proximity of the free surface. We observe that close to the surface the wave drag is of the order of the hydrodynamic drag. In our range of study, the measured force is more than one order smaller than predictions based on linear response. In order to investigate this discrepancy, we measure the amplitude of the waves at the origin of the wave drag, comparing the measurement with a theoretical model. The model captures the measurements at “large depth” but the wave’s amplitude saturates at “small depth,” an effect that partially accounts for the difference between the predicted and measured wave drag.
 Particulate, Multiphase, and Granular Flows

On the mixing induced by tightly confined spheres in bounded shear flows
View Description Hide DescriptionThe mixing of solute tracers produced by a dilute suspension of spheres undergoing shear flow is examined in the limit that the gap between the sphere and the bounding walls becomes vanishingly small. Such tight confinement produces an envelope of flipping trajectories in the vicinity of the sphere giving rise to swift mixing of an antisymmetric concentration distribution across the central plane of the gap. The size of this flipping envelope is demonstrated to be only weakly dependent on the angular velocity of the sphere and is accurately approximated by a two parameter model. This model can be used to calculate the additional mass transfer arising due to flipping. The degree of mixing in the system is directly related to the intensity of flipping which is shown to be a function of a single parameter χ given by where is the shear rate, a is the radius of the sphere, ϕs is the volume fraction of the spheres, and D is the diffusivity. As χ varies from 0 to ∞, the concentration distribution across the gap goes from being linear everywhere to being uniform across the flipping envelope, with the overall flux increasing by a factor of ∼3.

Coalescence and breakup of large droplets in turbulent channel flow
View Description Hide DescriptionCoalescence and breakup of large deformable droplets dispersed in a wallbounded turbulent flow are investigated. Droplets much larger than the Kolmogorov length scale and characterized by a broad range of surface tension values are considered. The turbulent field is a channel flow computed with pseudospectral direct numerical simulations, while phase interactions are described with a phase field model. Within this physically consistent framework, the motion of the interfaces, the capillary effects, and the complex topological changes experienced by the droplets are simulated in detail. An oilwater emulsion is mimicked: the fluids are considered of same density and viscosity for a range of plausible values of surface tension, resulting in a simplified system that sets a benchmark for further analysis. In the present conditions, the Weber number (We), that is, the ratio between inertia and surface tension, is a primary factor for determining the droplets coalescence rate and the occurrence of breakups. Depending on the value of We, two different regimes are observed: when We is smaller than a threshold value (We < 1 in our simulations), coalescence dominates until dropletdroplet interactions are prevented by geometric separation; when We is larger than the threshold value (We > 1), a permanent dynamic equilibrium between coalescence and breakup events is established.
 Laminar Flows

Dynamics of an inverted flexible plate in a uniform flow
View Description Hide DescriptionThe dynamics of an inverted flexible plate with a free leadingedge and a fixed trailingedge in a uniform flow has been studied numerically by an immersed boundarylattice Boltzmann method for the fluid flow and a finite element method for the plate deformation. Mechanisms underlying the dynamics of the fluidplate system are elucidated systematically. A series of distinct states of the plate deformation and motion are identified and can be described as straight, flapping, deflected, deflectedflapping, and asymmetricflapping states. Which state to occur depends mainly on the bending stiffness and aspect ratio of the plate. The forces exerted on the plate and the elastic strain energy of the plate are analyzed. It is found that the flapping state can improve the conversion of fluid kinetic energy to elastic strain energy. In addition, the effects of the mass ratio of the plate and the fluid, the Reynolds number, and the angle of attack of the uniform flow on the dynamics and the elastic strain energy of flexible plate are also investigated in detail. The vortical structures around the plate are given to discuss the connection of the evolution of vortices with the plate deformation and motion. The results obtained in this study provide physical insight into the understanding of the mechanisms on the dynamics of the fluidplate system.
 Instability and Transition

Instability mechanisms in a lowMachnumber reacting flow from coupled convectionreactiondiffusion equations
View Description Hide DescriptionIn this paper, instability mechanisms in a low Mach number reacting flow are investigated. Here, the emphasis is on the growth or decay of acoustic oscillations which arise from the acoustichydrodynamic interaction in a low Mach number reacting flow. Motivated by the studies in magnetohydrodynamics and atmospheric flows, we propose to investigate the acoustichydrodynamic coupling as a system of wavemean flow interaction. For example, a comparison with the heat fluctuation modified hydrodynamics associated with magnetohydrodynamics is useful in understanding this coupling. The wavelike acoustic disturbance is introduced here as a compressibility correction to the mean flow. Accounting for the multiple scales introduced by the weak compressibility, we derive a set of equations governing wavemean flow interaction in a reacting low Mach number flow. Sources such as volume expansion (which, in atmospheric flows arises due to the density variation with altitude) occur in reacting flows due to the heat release rate. This heat release rate, when coupled with the acoustic field, often leads to selfsustained thermoacoustic oscillations. In the study of such oscillations, we discover a relation between the acoustic pressure and second order thermal fluctuations. Further, using this relation, we discover the nonlinear coupling mechanism that would lead to selfsustained oscillations in a reacting low Mach number flow. This mechanism, represented by a coupled convection reaction diffusion system, is presented here for the first time. In addition to the acoustic pressure and temperature fields, we also discover the role of acoustic velocity field in the acoustichydrodynamic interaction through a convective and liftup mechanism.

Numerical investigation of binary fluid convection with a weak negative separation ratio in finite containers
View Description Hide DescriptionBy using a highorder compact finite difference method to solve the full hydrodynamic field equations, convection in binary fluid mixtures with a weak negative separation ratio of −0.1 in rectangular containers heated from below is numerically investigated. We consider the problem with the Prandtl number Pr ranging from 0.01 to 10 and the Lewis number Le from 0.0005 to 1. Several convective structures such as traveling wave, localized traveling wave, and undulation traveling wave convection as well as stationary overturning convection (SOC) are obtained. For the separation ratio considered, localized traveling wave state exists in a range of Rayleigh numbers spanning the critical point (the critical Rayleigh number at the onset of convection), and their length of the convective region is uniquely selected for a given parameter set. A bifurcation diagram of solution is drawn and the transitions between various traveling waves and the steady states on their upper branches are discussed. The effects of the fluid parameters and the aspect ratio of the container on the onset of convection and their saturated structures are studied in detail. Finally, several types of initial temperature fields are used to start simulations and five different stable SOC states with different mean wavenumbers are found. The corresponding heat and mass transfer properties of these stable SOC states are also investigated.
 Turbulent Flows

A comparison of opposition control in turbulent boundary layer and turbulent channel flow
View Description Hide DescriptionA comparison between classical opposition control applied in the configuration of a fully developed turbulent channel flow and applied locally in a spatially developing turbulent boundary layer is presented. It is found that the control scheme yields similar drag reduction rates if compared at the same friction Reynolds numbers. However, a detailed analysis of the dynamical contributions to the skin friction coefficient reveals significant differences in the mechanism behind the drag reduction. While drag reduction in turbulent channel flow is entirely based on the attenuation of the Reynolds shear stress, the modification of the spatial flow development is essential for the turbulent boundary layer in terms of achievable drag reduction. It is shown that drag reduction due to this spatial development contribution becomes more pronounced with increasing Reynolds number (up to Re τ = 660, based on friction velocity and boundary layer thickness) and even exceeds drag reduction due to attenuation of the Reynolds shear stress. In terms of an overall energy balance, it is found that opposition control is less efficient in the turbulent boundary layer due to the inherently larger fluctuation intensities in the near wall region.

Effects of cylinder Reynolds number on the turbulent horseshoe vortex system and near wake of a surfacemounted circular cylinder
View Description Hide DescriptionThe turbulent horseshoe vortex (HV) system and the nearwake flow past a circular cylinder mounted on a flat bed in an open channel are investigated based on the results of eddyresolving simulations and supporting flow visualizations. Of particular interest are the changes in the mean flow and turbulence statistics within the HV region as the necklace vortices wrap around the cylinder’s base and the variation of the mean flow and turbulence statistics in the near wake, in between the channel bed and the free surface. While it is well known that the drag crisis induces important changes in the flow past infinitely long circular cylinders, the changes are less understood and more complex for the case of flow past a surfacemounted cylinder. This is because even at very high cylinder Reynolds numbers, ReD, the flow regime remains subcritical in the vicinity of the bed surface due to the reduction of the incoming flow velocity within the bottom boundary layer. The paper provides a detailed discussion of the changes in the flow physics between cylinder Reynolds numbers at which the flow in the upstream part of the separated shear layers (SSLs) is laminar (ReD = 16 000, subcritical flow regime) and Reynolds numbers at which the transition occurs inside the attached boundary layers away from the bed and the flow within the SSLs is turbulent (ReD = 5 ∗ 10^{5}, supercritical flow regime). The changes between the two regimes in the dynamics and level of coherence of the largescale coherent structures (necklace vortices, vortex tubes shed in the SSLs and roller vortices shed in the wake) and their capacity to induce highmagnitude bed friction velocities in the mean and instantaneous flow fields and to amplify the nearbed turbulence are analyzed. Being able to quantitatively and qualitatively describe these changes is critical to understand Reynoldsnumberinduced scale effects on sediment erosion mechanisms around cylinders mounted on a loose bed, which is a problem of great practical relevance (e.g., for pier scour studies).

On the statistics of wind turbine wake meandering: An experimental investigation
View Description Hide DescriptionMeasurements of the instantaneous wake flow from a model wind turbine placed in a turbulent boundary layer were obtained by wallparallel oriented particle image velocimetry (PIV) in the St. Anthony Falls Laboratory wind tunnel. PIV velocity vector fields were used to investigate mean (expansion angle, wavelength, and wake velocity) and higher order statistics (local slope, curvature, and correlation) describing meandering motions in the turbine wake. These statistics were used to compare the wakes produced by four different wind turbine operating configurations, which include a single turbine operating at two different tipspeed ratios and two turbines aligned with the mean flow. The origin of meandering motions was identified for all cases in the hub vortex signature, which evolved into a stretched or compressed low speed meander in the wall parallel plane, depending on the turbine operating conditions and on the interaction with the wake shear layer. Finally, both autocorrelation and scaledependent statistics on the velocity minima fluctuations about the meander signature suggest that small scale vortices, found in the hub shear layer and in the wake shear layer, interact with the hub vortex and govern its spatial evolution into large scale wake meandering.

The triple decomposition of a fluctuating velocity field in a multiscale flow
View Description Hide DescriptionA new method for the triple decomposition of a multiscale flow, which is based on the novel optimal mode decomposition (OMD) technique, is presented. OMD provides low order linear dynamics, which fits a given data set in an optimal way and is used to distinguish between a coherent (periodic) part of a flow and a stochastic fluctuation. The method needs no external phase indication since this information, separate for coherent structures associated with each length scale introduced into the flow, appears as the output. The proposed technique is compared against two traditional methods of the triple decomposition, i.e., bin averaging and proper orthogonal decomposition. This is done with particle image velocimetry data documenting the near wake of a multiscale bar array. It is shown that both traditional methods are unable to provide a reliable estimation for the coherent fluctuation while the proposed technique performs very well. The crucial result is that the coherence peaks are not observed within the spectral properties of the stochastic fluctuation derived with the proposed method; however, these properties remain unaltered at the residual frequencies. This proves the method’s capability of making a distinction between both types of fluctuations. The sensitivity to some prescribed parameters is checked revealing the technique’s robustness. Additionally, an example of the method application for analysis of a multiscale flow is given, i.e., the phase conditioned transverse integral length is investigated in the near wake region of the multiscale object array.
 Compressible Flows

Particle response analysis for particle image velocimetry in supersonic flows
View Description Hide DescriptionWe examine the effects of compressibility, slip, and fluid inertia on the frequency response of particlebased velocimetry techniques for supersonic and hypersonic flows by solving the quasisteady drag equation for solid, spherical particles. We demonstrate that noncontinuum and fluid inertial effects significantly affect the particle response under all typical supersonic flow conditions. In particular, the particle frequency response obtained from a shock response test depends on the strength of the shock, decreasing with shock strength as noncontinuum effects become more prominent. For weak disturbances, such as those typical of turbulence, the actual particle frequency response can therefore be much lower than that obtained from a typical shock response. The greatest variability in the response was found to occur at low supersonic Mach numbers. The results were found to be typical of solid particles used for velocimetry under a wide range of wind tunnel conditions, and so, previous particle frequency response analyses based solely on shock response tests may well have overestimated the response to turbulence.

Study of two supersonic streamwise vortex interactions in a Mach 2.5 flow: Merging and no merging configurations
View Description Hide DescriptionThis work presents the detailed analysis of the flow fields resulting from two supersonic vortex interaction modes in a Mach 2.5 cold flow. The vortex interactions were selected beforehand by means of a reduced order modeling tool to obtain merging of the corotating structures in two counterrotating vortex pairs in one case and to prevent their merging in the second. To experimentally target the flow physics of interest, expansion ramps of the same height but different width and mutual distance were placed on the surface of a strut injector. The resulting flow fields have been characterized using stereoscopic particle image velocimetry surveys conducted at selected streamwise planes. Accurate measurements of the velocity and vorticity fields, strain rates, circulation, and the rate of change of the area of each vorticity patch in the surveyed flow highlight the differences between merging and nonmerging scenarios as well as the role of viscosity and turbulent diffusion in the resulting vortex dynamics. In particular, it is observed that, for the high Reynolds numbers typical of these supersonic flows and the associated time scales, an inviscid, nondiffusive formulation can be used for a reducedorder description that allows to capture the relevant dynamics related to the morphological distortion of the interacting streamwise vorticity patches introduced into the supersonic flow. The distribution of the strain rates in the flows resulting from the selected vortex configurations suggests that a faster mixing process may be expected in the merging case. However, the volumetric entrainment measurements show that the configuration in which merging was not attained yields a much larger entrainment of surrounding fluid compared to the merging case.
 Geophysical Flows

Bistability in inhomogeneity—Effects of flow coherent structures on the fate of a bistable reaction
View Description Hide DescriptionWe present a numerical study on the mixing process between two stable states of a chemical reaction model. The two stable states of the reactions are found in practice not to coexist, and a single stable state of homogeneous scalar concentration is achieved over long time. With all other parameters fixed, we find the dependence of the final state on the rate of reaction. Interestingly, with the existence of coherent structures, at a range of intermediate rate of reaction, we find that the final state also depends on the initial locations of the scalar impurity. The exact dependence on initial condition is explored in detail. These results lead to the fundamental understanding on the variability of biogeochemical tracers in the environment induced by nonlinear fluid stirring.

Highresolution simulations of downslope gravity currents in the acceleration phase
View Description Hide DescriptionGravity currents generated from an instantaneous buoyancy source propagating down a slope in the range of 0^{∘} ≤ θ < 90^{∘} have been investigated in the acceleration phase by means of highresolution twodimensional simulations of the incompressible NavierStokes equations with the Boussinesq approximation. Front velocity history shows that, after the heavy fluid is released from rest, the flow goes through the acceleration phase, reaching a maximum front velocity U f,max , and followed by the deceleration phase. The existence of a maximum of U f,max is found near θ = 40^{∘}, which is supported by the improved theory. It is identified for the first time that the time of acceleration decreases as the slope angle increases, when the slope angle is approximately greater than 10^{∘}, and the time of acceleration increases as the slope angle increases for gravity currents on lower slope angles. A fundamental difference in flow patterns, which helps explain the distinct characteristics of gravity currents on high and low slope angles using scaling arguments, is revealed. Energy budgets further show that, as the slope angle increases, the ambient fluid is more easily engaged in the gravitational convection and the potential energy loss is more efficiently converted into the kinetic energy associated with ambient fluid. The propagation of gravity currents on a slope is found to be qualitatively modified as the depth ratio, i.e., the lock height to channel height ratio, approaches unity. As the depth ratio increases, the conversion of potential energy loss into the kinetic energy associated with heavy fluid is inhibited and the conversion into the kinetic energy associated with ambient fluid is enhanced by the confinement of the top wall.

Numerical studies of thermal convection with temperature and pressuredependent viscosity at extreme viscosity contrasts
View Description Hide DescriptionMotivated by convection of planetary mantles, we consider a mathematical model for RayleighBénard convection in a basally heated layer of a fluid whose viscosity depends strongly on temperature and pressure, defined in an Arrhenius form. The model is solved numerically for extremely large viscosity variations across a unit aspect ratio cell, and steady solutions for temperature, isotherms, and streamlines are obtained. To improve the efficiency of numerical computation, we introduce a modified viscosity law with a low temperature cutoff. We demonstrate that this simplification results in markedly improved numerical convergence without compromising accuracy. Continued numerical experiments suggest that narrow cells are preferred at extreme viscosity contrasts, and this conclusion is supported by a linear stability analysis.