# Latest papers in fluid mechanics

### Lattice Boltzmann multicomponent model for direct-writing printing

We introduce a mesoscale approach for the simulation of multicomponent flows to model the direct-writing printing process, along with the early stage of ink deposition. As an application scenario, alginate solutions at different concentrations are numerically investigated alongside processing parameters, such as apparent viscosity, extrusion rate, and print head velocity. The present approach offers useful insights on the ink rheological effects upon printed products, susceptible to geometric accuracy and shear stress, by manufacturing processes such as the direct-writing printing for complex photonic circuitry, bioscaffold fabrication, and tissue engineering.

### Return to isotropy of homogeneous shear-released turbulence

Author(s): Ping-Fan Yang, Alain Pumir, and Haitao Xu

In homogeneous shear flow, turbulence exhibits anisotropic properties affecting all scales of motion at finite Reynolds numbers. Upon releasing the mean shear, the anisotropy characterizing the velocity field decays over a large eddy turnover time. The decay of the anisotropy of the vorticity field, however involves a range of time-scales, from the short (Kolmogorov) time scale, up to the large eddy turnover time.

[Phys. Rev. Fluids 6, 044601] Published Fri Apr 02, 2021

### Prediction of shock standoff distance with modified rotational relaxation time of air mixture

The rotational relaxation time of an air mixture is modified as an approach to improve accuracy when predicting hypersonic shock standoff distance. A novel atomistic quasi-classical trajectory (QCT) method with a modified approach is devised to drastically reduce computational cost, and rigorously model the rotational relaxation time of N2 in N2–N and N2–N2 collisions. The calculated full sets of rotational state-to-state transition rates obtained by the QCT method are fed into the rotational state-resolved master equations to determine the rotational relaxation time of N2. Clear discrepancies are observed when the present rotational relaxation time is compared with existing empirical data for N2. The existing empirical model is utilized to determine the rotational relaxation time of other atmospheric gas species. Then the present set of rotational relaxation times for the air mixture is employed to predict the hypersonic shock standoff distance over a blunt body of the ground and flight experiments. Compared with the results from the two-temperature model, the rotational nonequilibrium enlarges the hypersonic shock standoff distance. This increase in shock standoff distance by the rotational nonequilibrium is attributed to the delay in chemical reactions inside the shock layers. The accuracy of the predicted measured shock standoff distance is improved by considering the present rotational relaxation time of the air mixture.

### Erratum: “Data assimilation and resolvent analysis of turbulent flow behind a wall-proximity rib” [Phys. Fluids 31, 025118 (2019)]

### Designing a consistent implementation of the discrete unified gas-kinetic scheme for the simulation of three-dimensional compressible natural convection

Discrete unified gas-kinetic scheme (DUGKS) has been developed as a robust and accurate approach for thermal compressible flow simulations; however, designing an efficient and accurate lattice velocity model to take full advantage of DUGKS remains a challenge. In this study, we apply DUGKS to simulate three-dimensional compressible natural convection in an enclosure with a large temperature difference, without making the Boussinesq approximation. The Chapman–Enskog analysis indicates that the fourth-order moments of equilibrium is needed for the heat flux evaluation in the energy equation, implying that the fourth-order Hermite expansion of equilibrium and thus at least an eighth-order Gauss–Hermite quadrature are needed for accurate simulation of the Navier–Stokes–Fourier system. For this purpose, a highly efficient lattice velocity model, D3Q77A9, is derived, which provides a Gauss–Hermite quadrature of ninth-order accuracy in three dimensions. The accuracy of this D3Q77A9 model is demonstrated by simulating compressible natural convection flows in both two-dimensional and three-dimensional cavities. An error analysis is performed to emphasize the importance of combining a quadrature with an adequate degree of precision and a proper order of Hermite expansion of the equilibrium distribution.

### Turbulent flow characteristics around a non-submerged rectangular obstacle on the side of an open channel

The three-dimensional flow structure and turbulence characteristics around a non-submerged rectangular obstacle in an open channel are explored using numerical simulation. In particular, a low length-to-depth ratio condition, shown to be associated with three-dimensional flow features in our previous study, is considered. To sufficiently resolve all the important details of the three-dimensional turbulent flow around and in the entire wake of an obstacle, high-resolution large-eddy simulation (LES) employing is carried out on a parallel supercomputer. The LES results were compared with the measurements and analyzed to examine the horseshoe vortex structure, free-surface vortex structure, recirculation zones, vortex shedding process, turbulence characteristics, and wall shear stress distribution around an obstacle. The results provide important insights into the complete three-dimensional flow structure and wall shear stress patterns around the obstacle.

### Investigation of thermal large-eddy simulation approaches in a highly turbulent channel flow submitted to strong asymmetric heating

This study deals with thermal large-eddy simulation (T-LES) of anisothermal turbulent channel flow in the working conditions of solar receivers used in concentrated solar power towers. The flow is characterized by high-temperature levels and strong heat fluxes. The hot and cold friction Reynolds numbers of the simulations are, respectively, 630 and 970. The Navier–Stokes equations are solved under the low-Mach number approximation and the thermal dilatation is taken into account. The momentum convection and the density–velocity correlation subgrid terms are modeled. Functional, structural, and mixed subgrid-scale models are investigated. A tensorial version of the classical anisotropic minimum-dissipation (AMD) model is studied and produces good results. A Quick scheme and a second-order-centered scheme are tested for the discretization of the mass convection term. First, a global assessment of 22 large-eddy simulations is proposed, then six are selected for a careful analysis including profiles of mean quantities and fluctuation values as well as a comparison of instantaneous fields. Probability density functions of wall heat fluxes are plotted. The results point out that T-LESs performed with the Quick scheme tend to underestimate the wall heat flux whereas the second-order-centered scheme significantly improves its estimation. T-LESs tend to overestimate the peaks of velocity correlations. When regarding the dimensionless profiles of fluctuations, the tensorial AMD model provides better results than the other assessed models. For the heat flux estimation, the best agreement is found with the AMD model combined with the second-order-centered scheme.

### Hydrodynamic instability of free river bars

In this paper, we explore the hydrodynamic instability of free river bars driven by a weakly varying turbulent flow in a straight alluvial channel with erodible bed and non-erodible banks. We employ linear stability analysis in the framework of depth-averaged formulations for the hydrodynamics and the sediment transport. A significant fraction of the sediment flux is considered to be in suspension. The analysis is performed for the alternate pattern of river bars at the leading order followed by the next order, covering the effects of flow regime. We find that the unstable region bounded by a marginal stability curve depends significantly on the shear Reynolds number, which demarcates different flow regimes, and the Shields number and the relative roughness (particle size to flow depth ratio). The results at the next order stabilize the bars with longer wavenumbers. The variations of threshold aspect ratio with Shields number and relative roughness are studied for different flow regimes. In addition, for a given Shields number and relative roughness, the diagram of threshold aspect ratio vs shear Reynolds number is explained. Unlike the conventional theories of bar instability, the analysis reveals limiting values of Shields number and relative roughness beyond which the theoretical results at the next order produce infeasible regions of instability. The limiting values of Shields number and relative roughness appear to reduce, as the shear Reynolds number increases.

### Analytical solutions for the incompressible laminar pipe flow rapidly subjected to the arbitrary change in the flow rate

A one-dimensional mathematical model is developed for an unsteady incompressible laminar flow in a circular pipe subjected to a rapid change in the flow rate from an initial flow with flow rate, Qi, to a final flow with flow rate, Qf, in a step-like fashion at an arbitrary time, tc. The change in the flow rate may either be an increment, Qf > Qi, or a decrement, Qf < Qi. The change time, tc, may either belong to the initial flow remaining in a temporally developing state or temporally developed state. The developed model is solved using the Laplace transform method to deduce generalized analytical expressions for the flow characteristics, viz., velocity, pressure gradient, wall shear stress, and skin friction factor, [math], where Re is Reynolds number based on the cross-sectional area-averaged velocity and pipe radius. Exact solutions for [math] and [math] with [math] are available in the literature and the present generalized analytical solutions fill the remaining range of parameters, [math] and [math] with [math] and [math], where tsi is the time at which the initial flow reaches the temporally developed state. Exact solutions for canonical pipe flow problems reported in the literature are deduced as subsets of the derived generalized solutions. The parametric study reveals the effects of varying λa or λd and tc on the quantities of practical importance, viz., τs and [math], where τs is the time required for the final flow to reach the temporally developed state.

### The scales of the leading-edge separation bubble

The leading-edge separation bubble is a flow feature occurring on the suction side of thin foils as a result of separation at the sharp leading-edge followed by reattachment downstream along the chord. For a flat plate at zero angle of attack, the reattachment length of the bubble depends on the plate thickness t. At a nonzero incidence, instead, the underlying scale governing bubble length is not clear. To investigate, we undertake a critical review of experimental and theoretical studies and develop an analytical formulation to predict the reattachment length of plates both at zero and at small incidences. We focus on conditions where the bubble is turbulent, i.e., when transition occurs at a negligible distance from the point of separation. This occurs at thickness- and chord-based Reynolds numbers [math]. At angle of attack α = 0, we find that the reattachment length is [math] when the chord-to-thickness ratio is [math]. At [math], we find that [math], where [math] is the inverse of the growth rate of a turbulent free shear layer. These results allow estimating xR on the thin wings of, for example, aerial vehicles and yacht sails.

### Effects of slope and speed of escalator on the dispersion of cough-generated droplets from a passenger

During the pandemic of COVID-19, the public is encouraged to take stairs or escalators instead of elevators. However, the dispersion of respiratory droplets in these places, featured by slopes and human motion, is not well understood yet. It is consequently unclear whether the commonly recommended social-distancing guidelines are still appropriate in these scenarios. In this work, we analyze the dispersion of cough-generated droplets from a passenger riding an escalator with numerical simulations, focusing on the effects of the slope and speed of the escalator on the droplet dispersion. In the simulations, a one-way coupled Eulerian–Lagrangian approach is adopted, with the air-flow solved using the Reynolds-averaged Navier–Stokes method and the droplets modeled as passive Lagrangian particles. It is found that the slope alters the vertical concentration of the droplets in the passenger's wake significantly. The deflection of cough-generated jet and the wake flow behind the passenger drive the cough-generated droplets upwards when descending an escalator and downwards when ascending, resulting in both higher suspension height and larger spreading range of the viral droplets on a descending escalator than on an ascending one. These findings suggest that the present social-distancing guidelines may be inadequate on descending escalators and need further investigation.

### Numerical investigation of perfusion rates in the circle of Willis in different anatomical variations and ischemic stroke

The circle of Willis (CoW) is a set of arteries located in the basis of the brain. Prediction of perfusion rates and hemodynamics in the CoW is necessary to understand the relevant vascular diseases and to prescribe effective treatments. In this paper, the effect of ischemic stroke in the CoW is studied, taking into consideration the anatomical variations of the CoW. Moreover, an analysis on the effect of applied boundary conditions is carried out. To do so, a patient-specific model of the CoW is reconstructed from CT (computed tomography) images. Six different cases of boundary conditions are applied to complete and healthy CoW, and the flow rates are investigated. The proper pressure boundary conditions are then imposed to three other variations of the CoW, and the flow rates are compared. The results reveal that the overall inlet flow rate varies from 1.75% to 7.5% in three variations of healthy CoW. Moreover, the changes in flow rates of outlet and inlet branches are indicated in ischemic stroke by considering a spherical clot in the right middle cerebral artery (RMCA). In this case, the RMCA flow reduced by 88.4%, and the internal carotid artery flow decreased by 53.6%. These changes lead to increased flow rates of other inlets to support the brain; however, the overall inlet flow rate falls by 21.5%.

### Flow-induced vibrations of a pair of in-line square cylinders

Flow-induced bidirectional vibrations of two in-line square cylinders of same size and mass ratio ([math]) are analyzed at Reynolds number, Re = 100. The cylinders are located in the co-shedding regime, i.e., they are separated by a normalized center-to-center spacing of 5. The reduced speed, [math], is varied from 3 to 15 keeping Re constant. The upstream and downstream cylinders display identical frequency characteristics with [math]. Accordingly, the cylinders share identical decomposition of dynamic response. The response is composed of the desynchronization regimes and lower branch; an initial branch does not exist. The vibrations are hysteretic at the lock-in boundaries whereas for a single square oscillator, hysteresis is identified only near the onset of lock-in. Hysteresis in the solutions for [math] within the lower branch is reflected in the wake mode of the rear cylinder whereas for the upstream cylinder, wake mode remains identical. The vortex-induced vibration (VIV) of the upstream cylinder is qualitatively similar to that of an isolated square oscillator. Despite the range of lock-in of the cylinders being identical, the VIV of the downstream cylinder departs significantly from its upstream counterpart. The shear layers separated from the front cylinder impinge on the rear cylinder and alter its flow field. The rear cylinder executes high amplitude VIV over the entire lower branch. The symmetry of the drag-lift phase diagrams does not necessarily translate to symmetric phase plots of in-line and cross-stream response. The drag and in-line response of the cylinders are out of phase throughout.

### Intermittent unsteady propulsion with a combined heaving and pitching foil

Author(s): Emre Akoz, Amin Mivehchi, and Keith W. Moored

Aquatic animals swim with a wide range of kinematic motions affecting their shed vortex structures and propulsive performance. We explore the mechanistic trade-offs that occur when caudal fin swimmers use continuous or intermittent combined heaving and pitching motions. It is determined that intermittent swimming can improve efficiency for pitch dominated motions whereas heave dominated motions lead to higher efficiencies with continuous swimming. This phenomenon is a consequence of the physical origins of the force production for heave dominated and pitch dominated motions, which is discussed in light of unsteady thin airfoil theory.

[Phys. Rev. Fluids 6, 043101] Published Thu Apr 01, 2021

### Lagrangian heat transport in turbulent three-dimensional convection

Author(s): Philipp P. Vieweg, Christiane Schneide, Kathrin Padberg-Gehle, and Jörg Schumacher

Spatial regions that do not mix effectively with their surroundings in fully turbulent three-dimensional Rayleigh-Bénard convection are identified by clusters of Lagrangian trajectory segments. By monitoring a locally defined Nusselt number along these trajectories it is quantified that these Lagrangian coherent sets, which are indicated by the tracer clouds in the figures, contribute significantly less to the global heat transport than their spatial complement where thermal plumes rise and fall.

[Phys. Rev. Fluids 6, L041501] Published Thu Apr 01, 2021

### Active flow control of the dynamic wake behind a square cylinder using combined jets at the front and rear stagnation points

This study experimentally investigated an active flow control method with combined jets at the front and the rear stagnation points of a square cylinder to suppress the unsteady wake flow. The Reynolds number (Re) was [math], based on the incoming speed of airflow and the diameter of test model. The square cylinder model was manufactured with two narrow slots symmetrically positioned at the centerline of the front and rear surfaces. The strength of the jets is characterized with a dimensionless momentum coefficient [math]. We obtained the dynamic wake flow regimes by employing the particle image velocimetry technique. Then, with the method of proper orthogonal decomposition and linear stability analysis, the time-averaged flow characteristics, e.g., turbulence kinetic energy (TKE) and the Reynolds shear stress (RSS) distributions, and the dynamic wake flow behind the square cylinder were analyzed in detail. Results of flow visualization suggested that at low momentum coefficient [math] the wake flow regime showed no notable modifications to the wake. As [math] increased to 0.0948, the periodic shear layers from the square cylinder were found to be pushed to the farther wake. Meanwhile, the time-averaged wake flow region was found to be greatly modified in the streamwise direction with a notable decrease in TKE and RSS distributions. The experimental results indicated that unsteadiness of vortex shedding in the wake flow experienced notable suppression. For higher [math] up to 0.2133 and 0.3793, unsteady vortex shedding from the square cylinder and the dynamic wake flow were further suppressed in the near wake. A linear stability analysis was also employed to reveal the underlying nature of wake modification by the combined jets.

### Drag reduction of a blunt body through reconfiguration of rear flexible plates

We investigate the quasi-static reconfiguration of rear parallel flexible plates on the drag coefficient of a blunt body. The drag coefficient, plates deformation, and main features of the turbulent wake are characterized experimentally in a towing tank. It is found that increasing the flexibility of plates leads to an important drag reduction, induced by the progressive streamlining of the trailing edge due to plates deformation. The study of the Vogel exponent is adopted here to evaluate the limit on the potential drag reduction at large values of the Cauchy number, which is shown to be mainly caused by the growth in the vibrating amplitude response of plates. The plates deformation is analyzed by means of image processing, showing that their shapes mainly follow the first modal form of a cantilever beam deflection, although a slight concavity develops toward the plates tip for large Cauchy numbers. To further analyze this process, the empirical flow loading along the plates is estimated by a modified beam theory assuming a distributed load given by a power law. The experimental fitting shows that for large flexibility, the load diminishes at the rear tip. Besides, the progressive deformation of plates is shown to weaken the shedding of vortices and reduce the size of the recirculation bubble. Finally, an affine direct relationship between recirculation bubble aspect ratio and drag coefficient has been proposed in order to quantify the linkage between near wake modifications and hydrodynamic improvement provided by the trailing edge streamlining.

### Statistical properties of wave kinematics in long-crested irregular waves propagating over non-uniform bathymetry

Experimental and numerical evidence have shown that nonuniform bathymetry may alter significantly the statistical properties of surface elevation in irregular wave fields. The probability of “rogue” waves is increased near the edge of the upslope as long-crested irregular waves propagate into shallower water. The present paper studies the statistics of wave kinematics in long-crested irregular waves propagating over a shoal with a Monte Carlo approach. High order spectral method is employed as wave propagation model, and variational Boussinesq model is employed to calculate wave kinematics. The statistics of horizontal fluid velocity can be different from statistics in surface elevation as the waves propagate over uneven bathymetry. We notice strongly non-Gaussian statistics when the depth changes abruptly in sufficiently shallow water. We find an increase in kurtosis in the horizontal velocity around the downslope area. Furthermore, the effects of the bottom slope with different incoming waves are discussed in terms of kurtosis and skewness. Finally, we investigate the evolution of kurtosis and skewness of the horizontal velocity over a sloping bottom in a deeper regime. The vertical variation of these statistical quantities is also presented.

### Modeling of contactless bubble–bubble interactions in microchannels with integrated inertial pumps

In this study, the nonlinear effect of contactless bubble–bubble interactions in inertial micropumps is characterized via reduced parameter one-dimensional and three-dimensional computational fluid dynamics (3D CFD) modeling. A one-dimensional pump model is developed to account for contactless bubble-bubble interactions, and the accuracy of the developed one-dimensional model is assessed via the commercial volume of fluid CFD software, FLOW-3D. The FLOW-3D CFD model is validated against experimental bubble dynamics images as well as experimental pump data. Precollapse and postcollapse bubble and flow dynamics for two resistors in a channel have been successfully explained by the modified one-dimensional model. The net pumping effect design space is characterized as a function of resistor placement and firing time delay. The one-dimensional model accurately predicts cumulative flow for simultaneous resistor firing with inner-channel resistor placements (0.2L < x < 0.8L where L is the channel length) as well as delayed resistor firing with inner-channel resistor placements when the time delay is greater than the time required for the vapor bubble to fill the channel cross section. In general, one-dimensional model accuracy suffers at near-reservoir resistor placements and short time delays which we propose is a result of 3D bubble-reservoir interactions and transverse bubble growth interactions, respectively, that are not captured by the one-dimensional model. We find that the one-dimensional model accuracy improves for smaller channel heights. We envision the developed one-dimensional model as a first-order rapid design tool for inertial pump-based microfluidic systems operating in the contactless bubble–bubble interaction nonlinear regime.

### On the general analytic solution for unsteady turbulent incompressible flow between parallel plates

This research reports the mean-velocity field associated with a general plane-parallel flow, regardless of its being laminar, turbulent, steady-state, unsteady, or transient. The Reynolds-averaged Navier–Stokes equation is posed, with proper initial and boundary conditions, and the solution is developed in an easy-to-follow fashion. The time-dependent general analytic solution is obtained, which is the sum of three components: (i) the transient decay of the initial mean velocity, (ii) the unsteady mean velocity directly created by the mean pressure gradient, and (iii) the unsteady mean velocity originated from the flow's Reynolds shear-stress gradient. Each one of these components has a different evolution in time, resulting in an asynchronism among them that yields deformed mean-velocity profiles. The formalism is applied to study the transient flow created when an initial steady-state flow is accelerated or decelerated up to a final steady state. A rapidly accelerated version of this problem was already studied in a DNS by He and Seddighi [“Turbulence in transient channel flow,” J. Fluid Mech. 715, 60–102 (2013)]. We show that DNS results concerning mean velocity are qualitatively reproduced by our approach, including surprising features like the flattening of transient mean-velocity profiles, the middle mean-velocity overshoot, global laminarization, and the enhancement of the viscous sublayer related to the notion of hyperlaminarity already introduced by the authors. The decelerated case presents sharpening of mean-velocity profiles, middle mean-velocity undershoots, global turbulentization, and the destruction of the viscous sublayer, and poses predictions that await experimental confirmation. This research continues the exposition of the theory of underlying laminar flow initiated in previous papers.