# Latest papers in fluid mechanics

### Three-dimensional simulation of tracer transport dynamics in formations with high-permeability channels or fractures: Estimation of oil saturation

We simulate flow and dispersion of tracers in three-dimensional fractured geometries obtained with Voronoi tessellations. “Fractures” are generated and discretized using a parallel in-house code. These “fractures” can also be regarded as the high-permeability flow paths through the rock or a network of the “super-k” channels. The generated geometry contains multiply-connected matrix and fracture regions. The matrix region represents a porous rock filled with solid, water, and oil. Tracers diffuse in both regions, but advection is limited only to the fractures. The lattice-Boltzmann and random-walk particle-tracking methods are employed in flow and transport simulations. Mass-transfer across the matrix–fracture interface is implemented using the specular reflection boundary condition. Tracer partitioning coefficients can vary among the tracer compounds and in space. We use our model to match a field tracer injection test designed to determine remaining oil saturation. By analyzing the time-dependent behavior of the fully resolved, three-dimensional “fracture”–matrix geometry, we show that the industry-standard approach may consistently overestimate remaining oil saturation. For a highly heterogeneous reservoir system, the relative error of the field-based remaining oil estimates may exceed 50%.

### Onset of transition in the flow of polymer solutions through deformable tubes

Experiments are performed to investigate laminar-turbulent transition in the flow of Newtonian and viscoelastic fluids in soft-walled microtubes of diameter ∼400 μm by using the micro-particle image velocimetry technique. The Newtonian fluids used are water and water-glycerine mixtures, while the polymer solutions used are prepared by dissolving polyacrylamide in water. Using different tube diameters, elastic moduli of the tube wall, and polymer concentrations, we probe a wide range of dimensionless wall elasticity parameter Σ and dimensionless fluid elasticity number E. Here, Σ = (ρGR2)/η2, where ρ is the fluid density, G is the shear modulus of the soft wall, R is the radius of the tube, and η is the solution viscosity. The elasticity of the polymer solution is characterized by E = (λη0)/R2ρ, where λ is the zero-shear relaxation time, η0 is the zero-shear viscosity, ρ is the solution density, and R is the tube radius. The onset of transition is detected by a shift in the ratio of centerline peak to average velocity. A jump in the normalized centerline velocity fluctuations and the flattening of the velocity profile are also used to corroborate the onset of instability. Transition for the flow of Newtonian fluid through deformable tubes (of shear modulus ∼50 kPa) is observed at a transition Reynolds number of Ret ∼ 700, which is much lower than Ret ∼ 2000 for a rigid tube. For tubes of lowest shear modulus ∼30 kPa, Ret for Newtonian fluid is as low as 250. For the flow of polymer solutions in a deformable tube (of shear modulus ∼50 kPa), Ret ∼ 100, which is much lower than that for Newtonian flow in a deformable tube with the same shear modulus, indicating a destabilizing effect of polymer elasticity on the transition already present for Newtonian fluids. Conversely, we also find instances where flow of a polymer solution in a rigid tube is stable, but wall elasticity destabilizes the flow in a deformable tube. The jump in normalized velocity fluctuations for the flow of both Newtonian and polymer solutions in soft-walled tubes is much gentler compared to that for Newtonian transition in rigid tubes. Hence, the mechanism underlying the soft-wall transition for the flow of both Newtonian fluids and polymer solutions could be very different as compared to the transition of Newtonian flows in rigid pipes. When Ret is plotted with the wall elasticity parameter Σ for different moduli of the tube wall, by taking Newtonian fluids of different viscosities and polymer solutions of different concentrations, we observed a data collapse, with Ret following a scaling relation of Ret ∼ Σ0.7. Thus, both fluid elasticity and wall elasticity combine to trigger a transition at Re as low as 100 in the flow of polymer solutions through deformable tubes.

### Space-time correlations of velocity in a Mach 0.9 turbulent round jet

In a turbulent jet, the numerical investigation of space-time correlations C(r, τ) at two-point and two-time of streamwise fluctuating velocities is presented along the nozzle lipline. Large-eddy simulation (LES) is performed for a Mach 0.9 turbulent jet issuing from a round nozzle. The turbulent boundary layer is well developed at the nozzle outlet, upon the inner wall, by adopting synthetic turbulent inlet boundary conditions. We study the cross correlations of streamwise fluctuating velocities at three particular streamwise positions, i.e., x = 0.71, 7.03, and 34.47r0, corresponding to different stages of jet development, where r0 is the radius of the nozzle. Present results show that the classical Taylor’s frozen-flow model is unable to predict C(r, τ) accurately in this strongly spatially developing shear flow since the distortion of the flow pattern is missing. The isocorrelation contours of C(r, τ) show a clearly elliptical feature, which is found to be well predicted by the elliptic approximation (EA) model [G.-W. He and J.-B. Zhang, “Elliptic model for space-time correlations in turbulent shear flows,” Phys. Rev. E 73, 055303 (2006)]. According to the EA model, C(r, τ) has a scaling form of C(rE, 0) with two characteristic velocities U and V, i.e., rE = (r − Uτ)2 + V2τ2. By examining LES data, it is found that the characteristic velocity U determined in LES is in general consistent with the theoretical Ut in the EA model, while the trend of V in LES also matches with that of the theoretical Vt. Additionally, it is interesting that the ratio of V to Vt is approximately a constant V/Vt ≃ 1.3 in the turbulent jet.

### Statistical behaviors of conditioned two-point second-order structure functions in turbulent premixed flames in different combustion regimes

The second-order structure functions and their components conditioned upon various events have been analyzed for unweighted and density-weighted velocities using a Direct Numerical Simulation database. The heat release due to combustion has been shown to have significant influences on the structure functions and their components conditioned on different mixture states. The use of density-weighted velocities changes the relative magnitudes of differently conditioned structure functions but does not reduce the scatter of these magnitudes. The structure functions conditioned to constant-density unburned reactants at both points and normalized using the root-mean-square velocity conditioned to the reactants are larger at higher values of mean reaction progress variables [math] (deeper within the flame brush), with this trend being not weakened with increasing turbulence intensity u′/SL. These results indicate that, contrary to a common belief, combustion-induced thermal expansion can significantly affect the incoming constant-density turbulent flow of unburned reactants even at u′/SL and Karlovitz number Ka as large as 10 and 18, respectively. The statistical behaviors of the structure functions reveal that the magnitude of the flame normal gradient of the velocity component tangential to the local flame can be significant, and it increases with increasing turbulence intensity. Moreover, the structure functions conditioned on both points in the heat release zone bear the signature of the anisotropic effects induced by the baroclinic torque for the flames belonging to the wrinkled flamelet and corrugated flamelet regimes. These anisotropic effects weaken with increasing turbulence intensity in the thin reaction zone regime.

### Vortex-induced vibration and galloping of a circular cylinder in presence of cross-flow thermal buoyancy

The effect of cross-flow thermal buoyancy on vortex-induced vibration (VIV) of a circular cylinder is numerically investigated. An in-house fluid-structure solver based on the sharp-interface immersed boundary method is employed. The cylinder is kept in the uniform flow stream and is mounted elastically such that it is constrained to move in the transverse direction to the flow. The surface of the cylinder is heated at a prescribed temperature, and the thermal buoyancy is imposed in the transverse direction to the flow. Simulations are performed for the following parameters: Reynolds number Re = (50, 150), Prandtl number Pr = 7.1, mass ratio m = 2, reduced velocity UR = [4–15], and Richardson number Ri = [0–4]. We found that the thermal buoyancy could suppress or agitate the VIV. At lower Re (=50) and Ri = (1, 2), we observe the suppression in the VIV; however, there is no suppression for higher Re (=150) for these values of Ri. Galloping is observed for higher values of Ri = (3, 4) for Re = (50, 150). The galloping has been reported for rotationally asymmetric bluff bodies (e.g., D-section cylinder) in previous studies in isothermal flows. We show that a circular cylinder, a rotationally symmetric body, exhibits galloping due to the transversely acting thermal buoyancy at higher Ri.

### Formation, growth, and saturation of dry holes in thick liquid films under vapor-mediated Marangoni effect

Films and drops of liquids can change their shapes and move under the spatial gradient of surface tension. A remote volatile liquid of relatively low surface tension can induce such flows because its vapor locally lowers the surface tension of the films and drops. Here, we show that aqueous liquid films thicker than approximately 100 µm can be punctured to immediately expose a dry hole by an overhanging isopropyl alcohol drop, which is attributed to the vapor-mediated Marangoni effect. We construct and corroborate scaling laws to predict the film dynamics, considering the balance of the driving capillary force and resisting viscous and hydrostatic forces as well as the contact angle of the alcohol-adsorbed solid surface. This remote scheme to induce and sustain changes of liquid morphology can be applied for fluid sculpture and patterning for industrial and artistic practices.

### Rotating magnetic nanorods detect minute fluctuations of magnetic field

Author(s): Vaibhav Palkar, Pavel Aprelev, Arthur Salamatin, Artis Brasovs, Olga Kuksenok, and Konstantin G. Kornev

Magnetic nanorods rotating in a viscous liquid are very sensitive to any ambient magnetic field. We theoretically predicted and experimentally validated the conditions for two-dimensional synchronous and asynchronous rotation as well as three-dimensional precession and tumbling of nanorods in an amb...

[Phys. Rev. E 100, 051101(R)] Published Wed Nov 13, 2019

### Internal flow properties in a capillary bore

In this work, a detailed description of the internal flow field in a collapsing bore generated on a slope in a wave flume is given. It is found that in the case at hand, just prior to breaking, the shape of the free surface and the flow field below are dominated by capillary effects. While numerical approximations are able to predict the development of the free surface as it shoals on the laboratory beach, the internal flow field is poorly predicted by standard numerical models.

### Cross-stream migration and coalescence of droplets in a microchannel co-flow using magnetophoresis

Manipulation of aqueous droplets in microchannels has great significance in various emerging applications such as biological and chemical assays. Magnetic-field based droplet manipulation that offers unique advantages is consequently gaining attention. However, the physics of magnetic field-driven cross-stream migration and the coalescence of aqueous droplets with an aqueous stream are not well understood. Here, we unravel the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil based ferrofluid with a coflowing aqueous stream in the presence of a magnetic field. Our study reveals that the migration phenomenon is governed by the advection (τa) and magnetophoretic (τm) time scales. Experimental data show that the dimensionless equilibrium cross-stream migration distance δ* and the length [math] required to attain equilibrium cross-stream migration depend on the Strouhal number, St = (τa/τm), as δ* = 1.1 St0.33 and [math], respectively. We find that the droplet-stream coalescence phenomenon is underpinned by the ratio of the sum of magnetophoretic (τm) and film-drainage time scales (τfd) and the advection time scale (τa), expressed in terms of the Strouhal number (St) and the film-drainage Reynolds number (Refd) as ξ = (τm + τfd)/τa = (St−1 + Refd). Irrespective of the flow rates of the coflowing streams, droplet size, and magnetic field, our study shows that droplet-stream coalescence is achieved for ξ ≤ 50 and ferrofluid stream width ratio w* < 0.7. We utilize the phenomenon and demonstrated the extraction of microparticles and HeLa cells from aqueous droplets to an aqueous stream.

### Similarities between the structure functions of thermal convection and hydrodynamic turbulence

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

### Unidirectional large-amplitude oscillatory shear flow of human blood

Blood is a non-Newtonian suspension of red and white cells, platelets, fibrinogen, and cholesterols in Newtonian plasma. To assess its non-Newtonian behaviors, this work considers a newly proposed blood test, unidirectional large-amplitude oscillatory shear flow (udLAOS). In the laboratory, we generate this experiment by superposing LAOS onto steady shear flow in such a way that the shear rate never changes sign. It is thus intended to best represent the unidirectional pulsatile flow in veins and arteries. To model human blood, we consider the simplest model that can predict infinite-shear viscosity, the corotational Jeffreys fluid. We arrive at an exact analytical expression for the shear stress response of this model fluid. We discover fractional harmonics comprising the transient part of the shear stress response and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. We generalize the corotational Jeffreys fluid to multimode to best represent three blood samples from three healthy but different donors. To further improve our model predictions, we consider the multimode Oldroyd 8-constant framework, which contains the corotational Jeffreys fluid as a special case. In other words, by advancing from the multimode corotational Jeffreys fluid to the multimode Oldroyd 8-constant framework, five more model parameters are added, yielding better predictions. We find that the multimode corotational Jeffreys fluid adequately describes the steady shear viscosity functions measured for three different healthy donors. We further find that adding two more specific nonlinear constants to the multimode corotational Jeffreys fluid also adequately describes the behaviors of these same bloods in udLAOS. This new Oldroyd 5-constant model may find usefulness in monitoring health through udLAOS.

### Graeme A. Bird

### Graeme A. Bird

### Lagrangian coherent sets in turbulent Rayleigh-Bénard convection

Author(s): Christiane Schneide, Martin Stahn, Ambrish Pandey, Oliver Junge, Péter Koltai, Kathrin Padberg-Gehle, and Jörg Schumacher

Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh-Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number Ra=106 and at a Prandtl number Pr=10. Three different Lagrangian analysis techniqu...

[Phys. Rev. E 100, 053103] Published Mon Nov 11, 2019

### Flow analysis of a shock wave at pulse ionization: Riemann problem implementation

An experimental study of the plasma-gas dynamic fluid formed after pulse ionization of the gas flow with a plane shock wave with Mach number 2.2–4.8 is carried out. Nanosecond volume discharge with UV preionization was switched on when the shock moved in a tube channel test section. Energy input occurs in the low-pressure gas volume separated by the shock surface within a time less than 200–300 ns; a single shock wave breaks into three discontinuities in accordance with the 1D Riemann problem solution. The initial (plasma-dynamic) stage of the flow in the nanosecond time range is visualized by glow recording; the supersonic gas processes in the microsecond time range are recorded using high-speed shadow imaging. Quantitative information about the dynamics of the shocks and contact surface (plots of horizontal distance) was obtained within time up to 25 µs. A region with an increased gas-discharge plasma glow intensity, after the discharge electric current termination, was recorded in the time interval from 0.3 to 1.5 µs; it was explained by a jump in gas temperature and density between the new shock wave and the contact discontinuity.

### In-depth description of electrohydrodynamic conduction pumping of dielectric liquids: Physical model and regime analysis

In this work, we discuss the fundamental aspects of Electrohydrodynamic (EHD) conduction pumping of dielectric liquids. We build a mathematical model of conduction pumping that can be applied to all sizes, down to microsized pumps. In order to do this, we discuss the relevance of the Electrical Double Layer (EDL) that appears naturally on nonmetallic substrates. In the process, we identify a new dimensionless parameter related to the value of the zeta potential of the substrate-liquid pair, which quantifies the influence of these EDLs on the performance of the pump. This parameter also describes the transition from EHD conduction pumping to electro-osmosis. We also discuss in detail the two limiting working regimes in EHD conduction pumping: ohmic and saturation. We introduce a new dimensionless parameter, accounting for the electric field enhanced dissociation that, along with the conduction number, allows us to identify in which regime the pump operates.

### Eulerian conditional statistics of turbulent flow in a macroscale multi-inlet vortex chemical reactor

The conditional velocity time averages (⟨Ui|ξ⟩) and conditional mixture fraction time averages (⟨Φ|ωi⟩) were computed based on the Eulerian approach from the experimental data measured in a macroscale multi-inlet vortex chemical reactor. The conditioning events were determined by equally sized intervals of the sample space variable for the mixture fraction (ξ) and the velocity vector (ωi). The experimental data, which consisted of instantaneous velocities and concentration fields for two Reynolds numbers (Re = 3250 and 8125), were acquired using the simultaneous stereoscopic particle image velocimetry (stereo-PIV) and planar laser induced fluorescence techniques. Two mathematical models, the linear approximation and probability density function (PDF) gradient diffusion, were validated by experimental results. The results of the velocity conditioned on the mixture fraction demonstrated that the linear model works well in a low turbulence region away from the reactor center. Near the reactor center, high velocity gradients coupled with low concentration gradients reduce the accuracy of the linear model predictions. Nevertheless, an excellent agreement was found for the conditional events within ±2Φrms (mixture fraction root mean square). Due to lower concentration gradient in the tangential direction, the linear model better predicted the tangential velocity component for all locations investigated. The PDF model with an isotropic turbulent diffusivity performed inadequately for the tangential and axial velocity components. A modified version of the PDF model that considers the three components of the turbulent diffusivity produced a better agreement with the experimental data especially in the spiral arms regions of significant concentration gradients. Furthermore, the mixture fraction conditioned on the velocity vector components showed a more linear behavior near the reactor center, where the PDF of the mixture fraction is a Gaussian distribution. As the concentration gradients became prominent away from the reactor, ⟨Φ|ωi⟩ also deviated from the linear pattern. This was especially remarkable for the mixture fraction conditioned on the tangential velocity. The overall prediction of ⟨Φ|ωi⟩ improves at higher Reynolds number as the fluid mixing is enhanced.

### Intermittent locomotion of a self-propelled plate

Many fish and marine animals swim in a combination of active burst and passive coast phases, which is known as burst-and-coast swimming. The immersed boundary method was used to explore the intermittent locomotion of a three-dimensional self-propelled plate. The degree of intermittent locomotion can be defined in terms of the duty cycle (DC = Tb/Tf), which is the ratio of the interval of the burst phase (Tb) to the total flapping period (Tf = Tb + Tc), where Tc is the interval of the coast phase. The average cruising speed ([math]), the input power ([math]), and the swimming efficiency (η) were determined as a function of the duty cycle (DC). The maximum [math] arises for DC = 0.9, whereas the maximum η arises for DC = 0.3. The hydrodynamics of the intermittent locomotion was analyzed by examining the superimposed configurations of the plate and the phase map. The characteristics of the flapping motions in the burst and coast phases are discussed. A modal analysis was performed to examine the role of the flapping motion in the propulsion mechanism. The velocity map and the vortical structures are visualized to characterize qualitatively and quantitatively the influence of intermittent locomotion on propulsion.

### Exact moment analysis of transient dispersion properties in periodic media

This paper develops a homogenization approach, based on the introduction of exact local and integral moments, to investigate the temporal evolution of effective dispersion properties of point-sized and finite-sized particles in periodic media. The proposed method represents a robust and computationally efficient continuous approach, alternative to stochastic dynamic simulations. As a case study, the exact moment method is applied to analyze transient dispersion properties of point-sized and finite-sized particles in sinusoidal tubes under the action of a pressure-driven Stokes flow. The sinusoidal structure of the tube wall induces a significant variation of the axial velocity component along the axial coordinate. This strongly influences the transient behavior of the effective axial velocity [math] and of the dispersivity [math], both exhibiting wide and persistent temporal oscillations, even for a steady (not-pulsating) Stokes flow. For a pointwise injection of solute particles on the symmetry axis, many interesting features appear: negative values of the dispersion coefficient [math], values of [math] larger than the asymptotic value [math], and anomalous temporal scaling of the axial variance of the particle distribution. All these peculiar features found a physical and theoretical explanation by adopting simple transport models accounting for the axial and radial variation of the axial velocity field and its interaction with molecular diffusion.

### Effects of Reynolds number on vortex structure behind a surface-mounted finite square cylinder with AR = 7

This paper presents the numerical solutions of flow around a surface-mounted square cylinder of aspect ratio h/d = 7 at Reynolds numbers of 652 and 13 041. The aim is to investigate the effect of the Reynolds number, between its medium-to-high range, on the flow and vortex structure around such a cylinder. The present simulations have successfully reproduced the primary flow, as well as the three-dimensional large-scale vortex structure in the wake of the finite wall-mounted body. The observation of base vortices, tip vortices, and a horseshoe vortex is consistent with previous experimental studies. A dipole wake is captured at the higher Reynolds number, while a quadrupole wake is captured for the lower, indicating that the Reynolds number strongly influences the wake structure. In the near-wake region, by plotting the isosurface of instantaneous second invariant of the velocity gradient, the full-loop structure is observed for the quadrupole wake, while the half-loop structure is observed for the dipole wake. In the far-wake region, a braided vortex structure formed by asymmetric hairpin vortices is observed at both Reynolds numbers and a new wake topology is proposed for flows with a similar geometry.