Showing papers in "Physics of Fluids in 2014"

Sparsity-promoting dynamic mode decomposition

Abstract: Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsity-promoting variant of the standard DMD algorithm. Sparsity is induced by regularizing the least-squares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the l1-norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm well-suited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method.

Effect of the computational domain on direct simulations of turbulent channels up to Reτ = 4200

Abstract: The effect of domain size on direct numerical simulations of turbulent channels with periodic boundary conditions is studied. New simulations are presented up to Reτ = 4179 in boxes with streamwise and spanwise sizes of 2πh × πh, where h is the channel half-height. It is found that this domain is large enough to reproduce the one-point statistics of larger boxes. A simulation in a box of size 60πh × 6πh is used to show that a contour of the two-dimensional premultiplied spectrum of the streamwise velocity containing 80% of the kinetic energy closes at λx ≈ 100h.

Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to δ + ≈ 2000

Abstract: Two-point statistics are presented for a new direct simulation of the zero-pressure-gradient turbulent boundary layer in the range Re θ = 2780–6680, and compared with channels in the same range of Reynolds numbers, δ+ ≈ 1000–2000. Three-dimensional spatial correlations are investigated in very long domains to educe the average structure of the velocity and pressure fluctuations. The streamwise velocity component is found to be coherent over longer distances in channels than in boundary layers, especially in the direction of the flow. For weakly correlated structures, the maximum streamwise length is O ( 7 δ ) for boundary layers and O ( 18 δ ) for channels, attained at the logarithmic and outer regions, respectively. The corresponding lengths for the spanwise and wall-normal velocities and for the pressure are shorter, O ( δ -2δ). The correlations are shown to be inclined to the wall at angles that depend on the distance from the wall, on the variable being considered, and on the correlation level used to define them. All these features change little between the two types of flows. Most the above features are also approximately independent of the Reynolds number, except for the pressure, and for the streamwise velocity structures in the channel. Further insight into the flow is provided by correlations conditioned on the intensity of the perturbations at the reference point, or on their sign. The statistics of the new simulation are available in our website.

Dynamic mode decomposition for large and streaming datasets

Abstract: We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams. We present two algorithms: the first is mathematically equivalent to a standard “batch-processed” formulation; the second introduces a compression step that maintains computational efficiency, while enhancing the ability to isolate pertinent dynamical information from noisy measurements. Both algorithms reliably capture dominant fluid dynamic behaviors, as demonstrated on cylinder wake data collected from both direct numerical simulations and particle image velocimetry experiments.

An improved dynamic non-equilibrium wall-model for large eddy simulation

Abstract: A non-equilibrium wall-model based on unsteady 3D Reynolds-averaged Navier-Stokes (RANS) equations has been implemented in an unstructured mesh environment. The method is similar to that of the wall-model for structured mesh described by Wang and Moin [Phys. Fluids 14, 2043–2051 (2002)], but is supplemented by a new dynamic eddy viscosity/conductivity model that corrects the effect of the resolved Reynolds stress (resolved turbulent heat flux) on the skin friction (wall heat flux). This correction is crucial in predicting the correct level of the skin friction. Unlike earlier models, this eddy viscosity/conductivity model does not have a stress-matching procedure or a tunable free parameter, and it shows consistent performance over a wide range of Reynolds numbers. The wall-model is validated against canonical (attached) transitional and fully turbulent flows at moderate to very high Reynolds numbers: a turbulent channel flow at Reτ = 2000, an H-type transitional boundary layer up to Reθ = 3300, and a hig...

Physics of puffing and microexplosion of emulsion fuel droplets

Abstract: The physics of water-in-oil emulsion droplet microexplosion/puffing has been investigated using high-fidelity interface-capturing simulation. Varying the dispersed-phase (water) sub-droplet size/location and the initiation location of explosive boiling (bubble formation), the droplet breakup processes have been well revealed. The bubble growth leads to local and partial breakup of the parent oil droplet, i.e., puffing. The water sub-droplet size and location determine the after-puffing dynamics. The boiling surface of the water sub-droplet is unstable and evolves further. Finally, the sub-droplet is wrapped by boiled water vapor and detaches itself from the parent oil droplet. When the water sub-droplet is small, the detachment is quick, and the oil droplet breakup is limited. When it is large and initially located toward the parent droplet center, the droplet breakup is more extensive. For microexplosion triggered by the simultaneous growth of multiple separate bubbles, each explosion is local and independent initially, but their mutual interactions occur at a later stage. The degree of breakup can be larger due to interactions among multiple explosions. These findings suggest that controlling microexplosion/puffing is possible in a fuel spray, if the emulsion-fuel blend and the ambient flow conditions such as heating are properly designed. The current study also gives us an insight into modeling the puffing and microexplosion of emulsion droplets and sprays.

Roughness effects on wall-bounded turbulent flowsa)

Abstract: This paper outlines the authors' experimental research in rough-wall-bounded turbulent flows that has spanned the past 15 years. The results show that, in general, roughness effects are confined to the inner layer. In accordance with Townsend's Reynolds number similarity hypothesis, the outer layer is insensitive to surface condition except in the role it plays in setting the length and velocity scales for the outer flow. An exception to this can be two-dimensional roughness which has been observed in some cases to suffer roughness effects far from the wall. However, recent results indicate that similarity also holds for two-dimensional roughness provided the Reynolds number is large, and there is sufficient scale separation between the roughness length scale and the boundary layer thickness. The concept of similarity between smooth- and rough-wall flows is of great practical importance as most computational and analytical modeling tools rely on it either explicitly or implicitly in predicting flows over rough walls. Because of the observed similarity, the roughness function (ΔU+), or shift in the log layer, is a useful way of characterizing the roughness effect on the mean flow and the frictional drag. In the fully rough regime, it is shown that the hydraulic roughness length scale is related to the root-mean-square height (krms) and skewness (sk) of the surface elevation probability density function. On the other hand, the onset of roughness effects is seen to be associated with the largest surface features which are typified by the peak-to-trough height (kt). Roughness function behavior in the transitionally rough regime varies significantly between roughness types. Since no “universal” roughness function exists, no single roughness length scale can characterize all roughness types in all the flow regimes. Despite this, research using roughness with a systematic variation in texture is ongoing in an effort to uncover surface parameters that lead to the variation in the frictional drag behavior witnessed in the transitionally rough regime.

Drag reduction and the dynamics of turbulence in simple and complex fluidsa)

Abstract: Addition of a small amount of very large polymer molecules or micelle-forming surfactants to a liquid can dramatically reduce the energy dissipation it exhibits in the turbulent flow regime. This rheological drag reduction phenomenon is widely used, for example, in the Alaska pipeline, but it is not well-understood, and no comparable technology exists to reduce turbulent energy consumption in flows of gases, in which polymers or surfactants cannot be dissolved. The most striking feature of this phenomenon is the existence of a so-called maximum drag reduction (MDR) asymptote: for a given geometry and driving force, there is a maximum level of drag reduction that can be achieved through addition of polymers. Changing the concentration, molecular weight or even the chemical structure of the additives has little to no effect on this asymptotic value. This universality is the major puzzle of drag reduction. We describe direct numerical simulations of turbulent minimal channel flow of Newtonian fluids and viscoelasticpolymer solutions. Even in the absence of polymers, we show that there are intervals of “hibernating” turbulence that display very low drag as well as many other features of the MDR asymptote observed in polymer solutions. As Weissenberg number increases to moderate values the frequency of these intervals also increases, and a simple theory captures key features of the intermittent dynamics observed in the simulations. At higher Weissenberg number, these intervals are altered – for example, their duration becomes substantially longer and the instantaneous Reynolds shear stress during them becomes very small. Additionally, simulations of “edge states,” dynamical trajectories that lie on the boundary between turbulent and laminar flow, display characteristics that are similar to those of hibernating turbulence and thus to the MDR asymptote, again even in the absence of polymer additives. Based on these observations, we propose a tentative unified description of rheological drag reduction. The existence of MDR-like intervals even in the absence of additives sheds light on the observed universality of MDR and may ultimately lead to new flow control approaches for improving energy efficiency in a wide range of processes.

Comparison of direct numerical simulation databases of turbulent channel flow at Re τ = 180

Abstract: Direct numerical simulation (DNS) databases are compared to assess the accuracy and reproducibility of standard and non-standard turbulence statistics of incompressible plane channel flow at Re τ = 180. Two fundamentally different DNS codes are shown to produce maximum relative deviations below 0.2% for the mean flow, below 1% for the root-mean-square velocity and pressure fluctuations, and below 2% for the three components of the turbulent dissipation. Relatively fine grids and long statistical averaging times are required. An analysis of dissipation spectra demonstrates that the enhanced resolution is necessary for an accurate representation of the smallest physical scales in the turbulent dissipation. The results are related to the physics of turbulent channel flow in several ways. First, the reproducibility supports the hitherto unproven theoretical hypothesis that the statistically stationary state of turbulent channel flow is unique. Second, the peaks of dissipation spectra provide information on length scales of the small-scale turbulence. Third, the computed means and fluctuations of the convective, pressure, and viscous terms in the momentum equation show the importance of the different forces in the momentum equation relative to each other. The Galilean transformation that leads to minimum peak fluctuation of the convective term is determined. Fourth, an analysis of higher-order statistics is performed. The skewness of the longitudinal derivative of the streamwise velocity is stronger than expected (−1.5 at $y^{+}$ =30). This skewness and also the strong near-wall intermittency of the normal velocity are related to coherent structures.

Propulsive performance of unsteady tandem hydrofoils in an in-line configuration

Abstract: Experiments are reported on the behavior of two hydrofoils arranged in an in-line configuration as they undergo prescribed pitching motions over a wide range of phase lags and spacings between the foils. It is found that the thrust production and propulsive efficiency of the upstream foil differed from that of an isolated one only for relatively closely spaced foils, and the effects attenuated rapidly with increasing spacing. In contrast, the performance of the downstream foil depends strongly on the streamwise spacing and phase differential between the foils for all cases considered, and the thrust and propulsive efficiency could be as high as 1.5 times or as low as 0.5 times those of an isolated foil. Particle image velocimetry reveals how the wake interactions lead to these variations in propulsive performance, where a coherent mode corresponds to enhanced performance, and a branched mode corresponds to diminished performance.

A dynamic slip boundary condition for wall-modeled large-eddy simulation

Abstract: Wall models for large-eddy simulation (LES) are a necessity to remove the prohibitive resolution requirements of near-wall turbulence in high Reynolds turbulent flows. Traditional wall models often rely on assumptions about the local state of the boundary layer (e.g., logarithmic velocity profiles) and require a priori prescription of tunable model coefficients. In the present study, a slip velocity boundary condition for the filtered velocity field is obtained from the derivation of the LES equations using a differential filter. A dynamic procedure for the local slip length is additionally formulated making the slip velocity wall model free of any a priori specified coefficients. The accuracy of the dynamic slip velocity wall model is tested in a series of turbulent channel flows at varying Reynolds numbers and in the LES of a National Advisory Committee for Aeronautics (NACA) 4412 airfoil at near-stall conditions. The wall-modeled simulations are able to accurately predict mean flow characteristics, including the formation of a trailing-edge separation bubble in NACA 4412 configuration. The validation cases demonstrate the effectiveness of this wall-modeling approach in both attached and separated flow regimes.

Estimating uncertainties in statistics computed from direct numerical simulation

Abstract: Rigorous assessment of uncertainty is crucial to the utility of direct numerical simulation (DNS) results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier–Stokes equations. Due to the presence of non-trivial sampling error, standard techniques for estimating discretization error (such as Richardson extrapolation) fail or are unreliable. This work provides a systematic and unified approach for estimating these errors. First, a sampling error estimator that accounts for correlation in the input data is developed. Then, this sampling error estimate is used as part of a Bayesian extension of Richardson extrapolation in order to characterize the discretization error. These methods are tested using the Lorenz equations and are shown to perform well. These techniques are then used to investigate the sampling and discretization errors in the DNS of a wall-bounded turbulent flow at Reτ ≈ 180. Both small (Lx/δ × Lz/δ = 4π × 2π) and la...

Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection

Abstract: In this paper, we present numerical simulations of rapidly rotating Rayleigh-Benard convection in the Boussinesq approximation with stress-free boundary conditions. At moderately low Rossby number and large Rayleigh number, we show that a large-scale depth-invariant flow is formed, reminiscent of the condensate state observed in two-dimensional flows. We show that the large-scale circulation shares many similarities with the so-called vortex, or slow-mode, of forced rotating turbulence. Our investigations show that at a fixed rotation rate the large-scale vortex is only observed for a finite range of Rayleigh numbers, as the quasi-two-dimensional nature of the flow disappears at very high Rayleigh numbers. We observe slow vortex merging events and find a non-local inverse cascade of energy in addition to the regular direct cascade associated with fast small-scale turbulent motions. Finally, we show that cyclonic structures are dominant in the small-scale turbulent flow and this symmetry breaking persists in the large-scale vortex motion.

Dynamics of swimming bacteria at complex interfaces

Abstract: Flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces. Fluid dynamics predicts this circular motion to be clockwise (CW) above a rigid surface (when viewed from inside the fluid) and counter-clockwise (CCW) below a free surface. Recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation, both at solid surfaces absorbing slip-inducing polymers and interfaces covered with surfactants. Motivated by these results, we use a far-field hydrodynamic model to predict the kinematics of swimming near three types of interfaces: clean fluid-fluid interface, slipping rigid wall, and a fluid interface covered by incompressible surfactants. Representing the helical swimmer by a superposition of hydrodynamic singularities, we first show that in all cases the surfaces reorient the swimmer parallel to the surface and attract it, both of which are a consequence of the Stokes dipole component of the swimmer flow field. We then show that circular motion is induced by a higher-order singularity, namely, a rotlet dipole, and that its rotation direction (CW vs. CCW) is strongly affected by the boundary conditions at the interface and the bacteria shape. Our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria.

The jet in crossflow

Abstract: The jet in crossflow, or transverse jet, is a flowfield that has relevance to a wide range of energy and propulsion systems. Over the years, our group's studies on this canonical flowfield have focused on the dynamics of the vorticity associated with equidensity and variable density jets in crossflow, including the stability characteristics of the jet's upstream shear layer, as a means of explaining jet response to altered types of excitation. The jet's upstream shear layer is demonstrated to exhibit convectively unstable behavior at high jet-to-crossflow momentum flux ratios, transitioning to absolutely unstable behavior at low momentum flux and/or density ratios, with attendant differences in shear layer vorticity evolution and rollup. These differences in stability characteristics are shown to have a significant effect on how one optimally employs external excitation to control jet penetration and spread, depending on the flow regime and specific engineering application. Yet recent unexpected observations on altered transverse jet structure under different flow conditions introduce a host of unanswered questions, primarily but not exclusively associated with the nature of molecular mixing, that make this canonical flowfield one that is of great interest for more extensive exploration.

The formation mechanism and impact of streamwise vortices on NACA 0021 airfoil's performance with undulating leading edge modification

Abstract: Wings with tubercles have been shown to display advantageous loading behavior at high attack angles compared to their unmodified counterparts. In an earlier study by the authors, it was shown that an undulating leading-edge configuration, including but not limited to a tubercled model, induces a cyclic variation in circulation along the span that gives rise to the formation of counter-rotating streamwise vortices. While the aerodynamic benefits of full-span tubercled wings have been associated with the presence of such vortices, their formation mechanism and influence on wing performance are still in question. In the present work, experimental and numerical tests were conducted to further investigate the effect of tubercles on the flow structure over full-span modified wings based on the NACA 0021 profile, in the transitional flow regime. It is found that a skew-induced mechanism accounts for the formation of streamwise vortices whose development is accompanied by flow separation in delta-shaped regions near the trailing edge. The presence of vortices is detrimental to the performance of full-span wings pre-stall, however renders benefits post-stall as demonstrated by wind tunnel pressure measurement tests. Finally, primary and secondary vortices are identified post-stall that produce an enhanced momentum transfer effect that reduces flow separation, thus increasing the generated amount of lift.

Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture

Abstract: Direct numerical simulations of turbulent flow in a channel with superhydrophobic surfaces (SHS) were performed, and the effects of the surface texture on the turbulence and skin-friction coefficient were examined The SHS is modeled as a planar boundary comprised of spanwise-alternating regions of no-slip and free-slip boundary conditions Relative to the reference no-slip channel flow at the same bulk Reynolds number, the overall mean skin-friction coefficient is reduced by 216% A detailed analysis of the turbulence kinetic energy budget demonstrates a reduction in production over the no-slip phases, which is explained by aid of quadrant analysis of the Reynolds shear stresses and statistical analysis of the turbulence structures The results demonstrate a significant reduction in the strength of streamwise vortical structures in the presence of the SHS texture and a decrease in the Reynolds shear-stress component ⟨R 12⟩ which has a favorable influence on drag over the no-slip phases A secondary flow which is set up at the edges of the texture also effects a beneficial change in drag Nonetheless, the skin-friction coefficient on the no-slip features is higher than the reference levels in a simple no-slip channel flow The increase in the skin-friction coefficient is attributed to two factors First, spanwise diffusion of the mean momentum from free-slip to no-slip regions increases the local skin-friction coefficient on the edges of the no-slip features Second, the drag-reducing capacity of the SHS is further reduced due to additional Reynolds stresses, ⟨R 13⟩

Turbulent boundary layer flow over transverse aerodynamic roughness transitions: Induced mixing and flow characterization

Abstract: In studies of turbulent boundary layers at high Reynolds number, the term “roughness transition” is generally an implicit reference to the case of a streamwise step-change in roughness length (whether the roughness length is associated with surface fluxes of momentum, temperature, humidity, or some other quantity). This roughness configuration and flow response has received broad attention. Here, in contrast, we consider turbulent wall-bounded flows over transverse roughness transitions using large-eddy simulation. This is accomplished simply by aligning the boundary layer freestream direction parallel to momentum roughness length transitions, instead of perpendicular. In the present cases, the bounding surface is composed of two “high roughness” strips placed between three “low roughness” strips. The influences of two parameters are evaluated: (1) λ, the ratio of the high roughness length to the low roughness length; and (2) Ls, the width of the high roughness strips. In the immediate vicinity of the roughness change, the abrupt wallstress variation induces transverse turbulent mixing which is the source of a δ-scale secondary flow, recently described as a low momentum pathway (LMP) by Mejia-Alvarez et al. [“Structural attributes of turbulent flow over a complex topography,” Coherent Flow Structures at the Earth's Surface (Wiley-Blackwell, 2013), Chap. 3, pp. 25–42] and Mejia-Alvarez and Christensen [“Wall-parallel stereo PIV measurements in the roughness sublayer of turbulent flow overlying highly-irregular roughness,” Phys. Fluids, 25, 115109]. LMPs are spatially stationary and flanked by δ-scale counter-rotating vortices which serve to pump fluid vertically from the wall, ultimately leading to a spanwise variation in the boundary layer depth (for flows over surface roughness with a converging-diverging riblet pattern, spanwise variation of δ was also found in recent experiments by Nugroho et al. [“Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and direction surface roughness,” Int. J. Heat Fluid Flow 41, 90–102 (2013)]. Mean velocity and transverse Reynolds stresses are used to determine the mixing length associated with transverse mixing. In general, we find that variations in Ls and λ have a strong and mild impact on the secondary flow pattern, respectively.

Asymmetric steady streaming as a mechanism for acoustic propulsion of rigid bodies

Abstract: Recent experiments showed that standing acoustic waves could be exploited to induce self-propulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of an external oscillating velocity field. Steady streaming in the fluid, the inertial rectification of the time-periodic oscillating flow, generates steady stresses on the particle which, in general, do not average to zero, resulting in a finite propulsion speed along the axis of the symmetry of the particle and perpendicular to the oscillation direction. Our derivation of the propulsion speed is obtained at leading order in the Reynolds number and the deviation of the shape from that of a sphere. The results of our model are consistent with the experimental measurements, and more generally explains how time periodic forcing from an acoustic field can be harnessed to generate autonomous motion.

Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow

Abstract: Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of Re i = 105 for a radius ratio of η = r i /r o = 0.714 between the inner and outer cylinders. With increasing Re i , the flow undergoes transitions between three different regimes: (i) a flow dominated by large coherent structures, (ii) an intermediate transitional regime, and (iii) a flow with developed turbulence. In the first regime the large-scale rolls completely drive the meridional flow, while in the second one the coherent structures recover only on average. The presence of a mean flow allows for the coexistence of laminar and turbulent boundary layer dynamics. In the third regime, the mean flow effects fade away and the flow becomes dominated by plumes. The effect of the local driving on the azimuthal and angular velocity profiles is quantified, in particular, we show when and where those profiles develop.

Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction

Abstract: We derive and analyze a model for implicit Large Eddy Simulation (LES) of compressible flows that is applicable to a broad range of Mach numbers and particularly efficient for LES of shock-turbulence interaction. Following a holistic modeling philosophy, physically sound turbulence modeling and numerical modeling of unresolved subgrid scales (SGS) are fully merged, in a manner quite different from that of traditional implicit LES approaches. The implicit subgrid model is designed in such a way that asymptotic consistency with incompressible turbulence theory is maintained in the low Mach number limit. Compressibility effects are properly accounted for by a novel numerical flux function, which can capture strong shock waves in supersonic flows and also ensures an accurate representation of smooth waves and turbulence without excessive numerical dissipation. Simulations of shock-tube problems, Noh's three-dimensional implosion problem, large-scale forced and decaying three-dimensional homogeneous isotropic turbulence, supersonic turbulent boundary layer flows, and a Mach = 2.88 compression-expansion ramp flow demonstrate the good performance of the SGS model; across this range of flows, predictions are in excellent agreement with theory, direct numerical simulations, and experimental reference data. Results for implicit LES of canonical shock-turbulence interaction are compared with results of explicit LES using the dynamic Smagorinsky model. The analysis shows that details of the numerical method used for shock capturing clearly outweigh the effect of different turbulence modeling strategies in explicit and implicit LES. The implicit LES model recovers the ideal 2nd-order grid convergence of shock-capturing errors that has been predicted using Rapid Distortion Theory. The dynamic Smagorinsky model in conjunction with a hybrid method that combines sixth-order central differences with a seventh-order weighted essentially non-oscillatory scheme yields turbulence statistics that are very similar to the implicit LES results. However, while the explicit LES requires a tailored high-order low-dissipative numerical method that applies numerical dissipation only in shock normal direction, no such ad hoc adjustments are necessary with the proposed implicit LES method.

Turbulent intensity and Reynolds number effects on an airfoil at low Reynolds numbers

Abstract: This work investigates the aerodynamics of a NACA 0012 airfoil at the chord-based Reynolds numbers (Rec) from 5.3 × 103 to 2.0 × 104. The lift and drag coefficients, CL and CD, of the airfoil, along with the flow structure, were measured as the turbulent intensity Tu of oncoming flow varies from 0.6% to 6.0%. The analysis of the present data and those in the literature unveils a total of eight distinct flow structures around the suction side of the airfoil. Four Rec regimes, i.e., the ultra-low ( 5.0 × 106), are proposed based on their characteristics of the CL-Rec relationship and the flow structure. It has been observed that Tu has a more pronounced effect at lower Rec than at higher Rec on the shear layer separation, reattachment, transition, and formation of the separation bubble. As a result, CL, CD, CL/CD and their dependence on the airfoil angle of attack all vary with Tu. So does the critical Reynolds number Rec,cr that divides the ultra-low and low Rec regimes. It is further noted that the effect of increasing Tu bears similarity in many aspects to that of increasing Rec, albeit with differences. The concept of the effective Reynolds number Rec,eff advocated for the moderate and high Rec regimes is re-evaluated for the low and ultra-low Rec regimes. The Rec,eff treats the non-zero Tu effect as an addition of Rec and is determined based on the presently defined Rec,cr. It has been found that all the maximum lift data from both present measurements and previous reports collapse into a single curve in the low and ultra-low Rec regimes if scaled with Rec,eff.

Large eddy simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms

Abstract: In this study, we address the question of how kinetic energy is entrained into large wind turbine arrays and, in particular, how large-scale flow structures contribute to such entrainment Previous research has shown this entrainment to be an important limiting factor in the performance of very large arrays where the flow becomes fully developed and there is a balance between the forcing of the atmospheric boundary layer and the resistance of the wind turbines Given the high Reynolds numbers and domain sizes on the order of kilometers, we rely on wall-modeled large eddy simulation (LES) to simulate turbulent flow within the wind farm Three-dimensional proper orthogonal decomposition (POD) analysis is then used to identify the most energetic flow structures present in the LES data We quantify the contribution of each POD mode to the kinetic energy entrainment and its dependence on the layout of the wind turbine array The primary large-scale structures are found to be streamwise, counter-rotating vortices located above the height of the wind turbines While the flow is periodic, the geometry is not invariant to all horizontal translations due to the presence of the wind turbines and thus POD modes need not be Fourier modes Differences of the obtained modes with Fourier modes are documented Some of the modes are responsible for a large fraction of the kinetic energy flux to the wind turbine region Surprisingly, more flow structures (POD modes) are needed to capture at least 40% of the turbulent kinetic energy, for which the POD analysis is optimal, than are needed to capture at least 40% of the kinetic energy flux to the turbines For comparison, we consider the cases of aligned and staggered wind turbine arrays in a neutral atmospheric boundary layer as well as a reference case without wind turbines While the general characteristics of the flow structures are robust, the net kinetic energy entrainment to the turbines depends on the presence and relative arrangement of the wind turbines in the domain

The effectiveness of resistive force theory in granular locomotiona)

Abstract: Resistive force theory (RFT) is often used to analyze the movement of microscopic organisms swimming in fluids. In RFT, a body is partitioned into infinitesimal segments, each of which generates thrust and experiences drag. Linear superposition of forces from elements over the body allows prediction of swimming velocities and efficiencies. We show that RFT quantitatively describes the movement of animals and robots that move on and within dry granular media (GM), collections of particles that display solid, fluid, and gas-like features. RFT works well when the GM is slightly polydisperse, and in the “frictional fluid” regime such that frictional forces dominate material inertial forces, and when locomotion can be approximated as confined to a plane. Within a given plane (horizontal or vertical) relationships that govern the force versus orientation of an elemental intruder are functionally independent of the granular medium. We use the RFT to explain features of locomotion on and within granular media including kinematic and muscle activation patterns during sand-swimming by a sandfish lizard and a shovel-nosed snake, optimal movement patterns of a Purcell 3-link sand-swimming robot revealed by a geometric mechanics approach, and legged locomotion of small robots on the surface of GM. We close by discussing situations to which granular RFT has not yet been applied (such as inclined granular surfaces), and the advances in the physics of granular media needed to apply RFT in such situations.

Skin-friction drag reduction in the turbulent regime using random-textured hydrophobic surfaces

Abstract: Technologies for reducing hydrodynamic skin-friction drag have a huge potential for energy-savings in applications ranging from propulsion of marine vessels to transporting liquids through pipes. The majority of previous experimental studies using hydrophobic surfaces have successfully shown skin-friction drag reduction in the laminar and transitional flow regimes (typically Reynolds numbers less than ≃106 for external flows). However, this hydrophobicity induced drag reduction is known to diminish with increasing Reynolds numbers in experiments involving wall bounded turbulent flows. Using random-textured hydrophobic surfaces (fabricated using large-length scalable thermal spray processes) on a flat plate geometry, we present water-tunnel test data with Reynolds numbers ranging from 106 to 9 × 106 that show sustained skin-friction drag reduction of 20%–30% in such turbulent flow regimes. Furthermore, we provide evidence that apart from the formation of a Cassie state and hydrophobicity, we also need a low surface roughness and an enhanced ability of the textured surface to retain trapped air, for sustained drag reduction in turbulent flow regimes. Specifically, for the hydrophobic test surfaces of the present and previous studies, we show that drag reduction seen at lower Reynolds numbers diminishes with increasing Reynolds number when the surface roughness of the underlying texture becomes comparable to the viscous sublayer thickness. Conversely, test data show that textures with surface roughness significantly smaller than the viscous sublayer thickness and textures with high porosity show sustained drag reduction in the turbulent flow regime. The present experiments represent a significant technological advancement and one of the very few demonstrations of skin-friction reduction in the turbulent regime using random-textured hydrophobic surfaces in an external flow configuration. The scalability of the fabrication method, the passive nature of this surface technology, and the obtained results in the turbulent regime make such hydrophobic surfaces a potentially attractive option for hydrodynamic skin-friction drag reduction.

Large-eddy simulation of turbulent cavitating flow in a micro channel

Abstract: Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data of the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.

On the influence of outer large-scale structures on near-wall turbulence in channel flow

Abstract: Direct Numerical Simulation (DNS) data for channel flow at 1025 are used to analyse the interaction between large outer scales in the log-law region – referred to as super-streaks – and the small-scale, streaky, streamwise-velocity fluctuations in the viscosity-affected near-wall layer. The study is inspired by extensive experimental investigations by Mathis, Marusic, and Hutchins, culminating in a predictive model that describes, in a supposedly universal manner, the “footprinting” and “modulating” effects of the outer structures on the small-scale near-wall motions. The approach used herein is based on the examination of joint PDFs for the small-scale fluctuations, conditioned on regions of large-scale footprints. The large and small scales are separated by means of the Huang-Hilbert empirical-mode decomposition, the validity of which is demonstrated by way of pre-multiplied energy spectra, correlation maps, and energy profiles for both scales. Observations derived from the PDFs then form the basis of assessing the validity of the assumptions underlying the model. Although the present observations support some elements of the model, the results imply that modulation by negative and positive large-scale fluctuations differ greatly – an asymmetric response that is not compatible with the model. The study is thus extended to examining the validity of an alternative proposal, which is based on the assumption that a universal description of the small-scale response to the large-scale motions has to rely on the velocity fluctuations being scaled with the large-scales-modified local friction velocity, rather than with the mean value. This proposal is partially supported by the present analysis. Finally, an alternative, new phenomenological model is proposed and examined.

The water entry of slender axisymmetric bodies

Abstract: We present a study of the forces, velocities, and trajectories of slender (length/diameter = 10) axisymmetric projectiles using an embedded inertial measurement unit (IMU). Three nose shapes (cone, ogive, and flat) were used. Projectiles were tested at vertical and oblique impact angles with different surface treatments. The trajectory of a half-hydrophobic and half-hydrophilc case impacting vertically was compared to the trajectory of symmetrically coated projectiles impacting the free surface at oblique angles. The oblique impact cases showed significantly more final lateral displacement than the half-and-half case over the same depth. The amount of lateral displacement was also affected by the nose shape, with the cone nose shape achieving the largest lateral displacement for the oblique entry case. Instantaneous lift and drag coefficients were calculated using data from the IMU for the vertical, half-and-half, and oblique entry cases. Impact forces were calculated for each nose shape and the flat nose shape experienced the largest impulsive forces up to 37 N when impacting vertically. The impact force of the flat nose decreased for the oblique entry case. The location of the center of pressure was determined at discrete time steps using a theoretical torque model and values from the IMU. Acoustic spectrograms showed that the sound produced during the water entry event predominately arises from the pinch-off for the cone and ogive nose shapes, with additional sound production from impact for the flat nose shape. Each test run was imaged using two Photron SA3 cameras.

Mobilization of a trapped non-wetting fluid from a three-dimensional porous medium

Abstract: We use confocal microscopy to directly visualize the formation and complex morphologies of trapped non-wetting fluid ganglia within a model 3D porous medium. The wetting fluid continues to flow around the ganglia after they form; this flow is characterized by a capillary number, Ca. We find that the ganglia configurations do not vary for small Ca; by contrast, as Ca is increased above a threshold value, the largest ganglia start to become mobilized and are ultimately removed from the medium. By combining our 3D visualization with measurements of the bulk transport, we show that this behavior can be quantitatively understood by balancing the viscous forces exerted on the ganglia with the pore-scale capillary forces that keep them trapped within the medium. Our work thus helps elucidate the fluid dynamics underlying the mobilization of a trapped non-wetting fluid from a 3D porous medium.

Hydrodynamic tracer diffusion in suspensions of swimming bacteria

Abstract: We present theoretical predictions, simulations, and experimental measurements of the diffusion of passive, Brownian tracer particles in the bulk of three-dimensional suspensions of swimming bacteria performing run-tumble random walks. In the theory, we derive an explicit expression for the “hydrodynamic” tracer diffusivity that results from the fluid disturbances created by a slender-body model of bacteria by ensemble averaging the mass conservation equation of the tracer over the space of tracer-bacterium interactions which are assumed to be binary. The theory assumes that the orientations of the bacterium before and after a tumble are uncorrelated and the fluid velocity disturbance created by the bacterium is small compared to its swimming speed. The dependence of the non-dimensional hydrodynamic diffusivity Dh obtained by scaling the dimensional hydrodynamic diffusivity by nL3UsL on the persistence in bacterial swimming and the Brownian diffusivity of the tracer are studied in detail through two nond...