# Latest papers in fluid mechanics

### Three-dimensional printing of diamagnetic microparticles in paramagnetic and diamagnetic media

We present an analytical model that explains the motion of finite-size diamagnetic particles in paramagnetic or diamagnetic fluid media. Our model problem is the magnetic field-assisted three-dimensional assembly of carboxylate microspheres in a gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) solution that is placed in a cuboid. The trajectory of each microparticle is determined through a time marching solution of its equation of motion. The effects of the (1) magnetic field distribution and (2) magnetic susceptibility of the paramagnetic solution, which depends on the Gd-DTPA concentration, on the dynamics of particle assembly are identified. Validation of the analytical model is provided through experimental measurements. For the first time, we demonstrate that it is possible to form structures of diamagnetic particles in diamagnetic fluid media, for which we select the assembly of graphene in water.

### Flow-induced vibration of inherently nonlinear structures with applications in energy harvesting

This paper proposes a novel design for a flow-induced vibration-based energy harvester, consisting of an elastic L-shaped beam, with an inherent nonlinearity in its structural stiffness as an alternative to the classical cantilever beam used in conventional fluidic energy harvester designs. The L-shaped beam supports a prism at its tip and undergoes large-amplitude galloping oscillations. The results from wind tunnel experiments show that by replacing a conventional linear structure that supports the prism with a nonlinear one, the high frequency flow components, shed from the tip prism, were capable of exciting the oscillations of the structure at higher harmonics of the main resonance, thus enhancing the power density of the energy harvester. As a result of improved power density values, the proposed harvester design holds great potential to be used as advanced space-efficient energy harvesters.

### Influence of glow discharge on evolution of disturbance in a hypersonic boundary layer: The effect of second mode

This is the companion volume on the effects of artificial disturbance on the transition process of a boundary layer over a flat plate. The artificial disturbance with the frequency in the range of second-mode instability is introduced into the boundary layer by glowing discharge on the surface of the plate. Experiments are performed using Rayleigh-scattering visualization, wall pressure pulsations measurement, and high-frequency schlieren visualization in the Φ300 mm hypersonic quiet wind tunnel at Peking University. It is found that the second-mode instability waves are stimulated remarkably by the artificial disturbance, and the boundary layer transition is triggered effectively. The second-mode instability interacts with the first mode via a phase-lock mechanism, which leads to the rapid amplification of the first mode and the moving forward of transition location.

### Behavior of particle swarms at low and moderate Reynolds numbers using computational fluid dynamics—Discrete element model

In the present study, the sedimentation of a swarm of mono-sized particles is investigated using the Computational Fluid Dynamics–Discrete Element Model (CFD-DEM) approach. The computational approach employed was able to accurately predict the breakup pattern of the swarm of particles into secondary clusters. The rate of leakage of the particles from the cluster (in the creeping flow regime) was found to linearly increase with an increase in the initial number of particles present in the sedimenting cluster. The breakup pattern of the cluster of particles was found to be highly sensitive to the shape of the outer domain. At Rec = 5, the sedimentation of the cluster in a cylindrical outer domain was observed to break up into six secondary blobs (k = 6), whereas for a square and a rectangular outer domain, the breakup resulted in four (k = 4) and two (k = 2) secondary blobs, respectively. Besides, the CFD-DEM approach was found to be in excellent agreement with the experimental data as opposed to the Oseenlet point particle approach, which could not accurately predict the settling velocities for a sedimenting cluster at a finite Rec and high solid fraction (Rec = 14, ϕs ≈ 0.5).

### Two-equation and multi-fluid turbulence models for Richtmyer–Meshkov mixing

This paper concerns an investigation of two different approaches in modeling the turbulent mixing induced by the Richtmyer–Meshkov instability (RMI): A two-equation K-L multi-component Reynolds-averaged Navier–Stokes model and a two-fluid model. We have improved the accuracy of the K-L model by implementing new modifications, including a realizability condition for the Reynolds stress tensor and a threshold in the production of the turbulence kinetic energy. We examine the models in the one-dimensional (1D) form in the (re)-shocked mixing of a double-planar air and sulfur-hexafluoride (SF6) interface of the Atwood number |At| ≃ 0.6853. Furthermore, we investigated the models’ accuracy to RMI-induced mixing of a (re)-shocked planar-inverse chevron air–SF6 interface. Relevant integral quantities in time, as well as instantaneous profiles and contour plots, are used to assess the models’ accuracy against high-resolution implicit large eddy simulations. The proposed modifications improve the efficiency of the K-L model. The model is designed as a simple model capable of capturing the self-similar growth of Rayleigh–Taylor and Richtmyer–Meshkov flows. The two-fluid model remains more accurate but is also computationally more expensive.

### Drop-in additives for suspension manipulation: Colloidal motion induced by sedimenting soluto-inertial beacons

Author(s): Anirudha Banerjee, Huanshu Tan, and Todd M. Squires

A 1-micron Brownian colloid on a random walk can take more than a month to traverse a 1 mm distance. We present a strategy for a drop-in additive to induce spontaneous migration of particles in a suspension at a rate orders of magnitude faster than simple diffusion. The additive, referred to as a solutoinertial beacon, releases a solute as it sediments within the suspension. This solute flux propels colloids to migrate via diffusiophoresis. Theoretical and scaling analyses capture the experimental observations well and reveal design parameters that govern the dynamics of particle motion.

[Phys. Rev. Fluids 5, 073701] Published Thu Jul 02, 2020

### Actuation response model from sparse data for wall turbulence drag reduction

Author(s): Daniel Fernex, Richard Semaan, Marian Albers, Pascal S. Meysonnat, Wolfgang Schröder, and Bernd R. Noack

Drag reduction of an actuated turbulent boundary layer at a momentum-thickness-based Reynolds number Reθ = 1000 is computed, modeled, and predicted. The drag reduction for the set of actuation parameters is modeled using 71 large-eddy simulations. This drag model allows extrapolation outside the actuation domain for larger wavelengths and amplitudes. The modeling novelty combines support vector regression for interpolation, a parametrized ridgeline leading out of the data domain, a scaling for the drag reduction, and a discovered self-similar structure of the actuation effect.

[Phys. Rev. Fluids 5, 073901] Published Thu Jul 02, 2020

### Decaying two-dimensional turbulence undergoes statistical heating

Author(s): J. G. Esler and R. K. Scott

Simulations of decaying two-dimensional turbulence show a persistent trend in the statistical temperature, from “colder” states in which dipoles are prevalent, to “hotter” states dominated by clusters of like-signed vortices. The spontaneous heating effect is shown to be consistent with a decay law for the vortex number density that is faster than the t−2/3 law deduced from similarity arguments.

[Phys. Rev. Fluids 5, 074601] Published Thu Jul 02, 2020

### On sustaining turbulence production in interacting supersonic streamwise vortices

Interacting supersonic streamwise vortices have been investigated as a means to enhance mixing at supersonic velocities. However, the turbulence dynamics associated with this class of flow has been left largely unexplored despite turbulence playing a major role in the achievement of molecular mixing. For this reason, the process of turbulent kinetic energy production in interacting supersonic streamwise vortices is investigated in this work. Specifically, the link between the mean flow motion and turbulence, represented by the production term of the turbulent transport equation, is analyzed. An approach is proposed in which the mean flow strain rates can be cast such that their intensity and morphology properly couple with the requirements imposed by the Reynolds stresses that, in the framework of this work, are shown to be intimately linked with the resulting plume morphology. The analysis is leveraged for the design of a mode of vortex interaction targeted to maintain a positive production of turbulent kinetic energy in the downstream evolution. The resulting configuration was experimentally investigated in a Mach 2.5 flow by stereoscopic particle image velocimetry. The results from these experiments show that the turbulence production remained positive and sustained turbulence levels, a unique result in the available literature. The role of turbulence anisotropy and the principal direction of negative planar strain rates are highlighted in detail in this work.

### Passive control of coaxial jet with supersonic primary jet and sonic secondary jet

The mixing enhancement of a coaxial jet with a Mach 1.4 primary jet and sonic secondary jet, at different convective Mach numbers, is presented in this study. Rectangular tabs of aspect ratios (AR = h/[math], where h and [math] are the tab height and width, respectively) 2.0 and 0.75 were employed to manipulate the primary and secondary jets, respectively. The primary jet (C0) and coaxial jet without control or manipulation (C1) are studied in order to decouple the effects of rectangular tabs on jet mixing. Four different tab configurations were studied, viz., tabs placed in the primary jet (C2), tabs placed in the secondary jet (C3), and tabs placed in both primary and secondary jets with the relative orientation between them of 0° (C4) and 90° (C5), to document the effect of tabs on mixing. The supersonic core length [math] of the manipulated jet was used as a measure to quantify the mixing performance of the manipulated jet. The secondary flow reduces the growth rate of the primary shear layer and elongates the supersonic core length. This study reveals that the manipulated jet emulates the characteristic of a non-circular jet. Primary tabs are highly effective in reducing the supersonic core length of the coaxial jet than secondary tabs, and hence, the jet mixing increases. Two different flow categories of the manipulated jet have been identified. The physical reason behind the observed jet mixing and flow categories have been presented based on arguments related to changes in the flow field and shock structure.

### On the use of leading-edge serrations for noise control in a tandem airfoil configuration

Passive noise control for a tandem NACA 65-710 airfoil configuration is experimentally investigated by applying leading-edge serrations on the rear airfoil. With a sliding side-plate mechanism that allows the rear airfoil to move in the vertical direction relative to the front airfoil, the position of maximum turbulence interaction noise is first identified from the far-field noise measurements. Subsequently, detailed static surface pressure distribution and unsteady surface pressure fluctuations are acquired to shed more light on the physical phenomenon and underlying noise-reduction mechanism of the leading-edge serrations. The far-field noise measurements confirm that a notable turbulence interaction noise reduction can be achieved from 600 Hz < f < 3000 Hz, agreeing well with the previous literature on the effectiveness of the leading-edge serrations. The near-field hydrodynamic analyses obtained using remote-sensing techniques of the fluctuating pressure fields over the airfoil show that a significant reduction in the surface pressure fluctuation levels up to 20 dB/Hz can be observed at the serrated-tip plane of the rear serrated airfoil close to the leading-edge regions, over the range of frequencies investigated. Although reduction can also be observed on the serrated-root plane, the magnitude is much less significant. The present results suggest that the modification of the unsteady loading on the rear airfoil by the leading-edge serrations plays a crucial role in the reduction of turbulence interaction noise in the tandem airfoil configuration, which may find practical application for noise reduction in aerodynamic systems involving rows of airfoils, such as contra-rotating open rotors and outlet guide vanes.

### Analytical study of an effect of gas compressibility on a burning accident in an obstructed passage

The incompressible analytical formulation describing a burning accident in an obstructed passage [F. Kodakoglu et al., “Towards descriptive scenario of a burning accident in an obstructed mining passage: An analytical approach,” in 27th International Colloquium on the Dynamics of Explosions and Reactive Systems (ICDERS), Beijing, China, July 28–Aug 2, 2019, Paper 369] is extended to account for gas compression, which cannot be ignored as soon as the flame velocity starts approaching the speed of sound. The analysis combines the theories of globally spherical, self-accelerating premixed expanding flames with that of ultrafast flame acceleration in obstructed conduits. It is shown that while the entire acceleration scenario may promote the flame velocity up to near-sonic values, the effect of gas compressibility moderates flame acceleration, and such an impact depends strongly on various thermal-chemical properties of the combustible premixture. Starting with gaseous combustion, the formulation is subsequently widened to the gaseous-dusty environments with combustible (coal) and inert (sand) dusts, and their combinations. In particular, it is quantified how the flame evolution and its locus and velocity depend on the type and size of the dust particles.

### Stealthy movements and concealed swarms of swimming micro-robots

Here, we show that micro-swimmers can form a concealed swarm through synergistic cooperation in suppressing one another’s disturbing flows. We then demonstrate how such a concealed swarm can actively gather around a favorite spot, point toward a target, or track a desired trajectory in space, while minimally disturbing the ambient fluid. Our findings provide a clear road map to control and lead flocks of swimming micro-robots in stealth vs fast modes, tuned through their active collaboration in minimally disturbing the host medium.

### Influence of viscoelasticity on mixing performance of primary and secondary circulation flows in stirred vessels

The aim of this study was to experimentally verify the mixing performance of primary and secondary circulation flows appearing in turbulence in stirred vessels of Newtonian and viscoelastic fluids. Impeller torque measurements, flow visualization, and particle image velocimetry and planar laser-induced fluorescence measurements were performed. In the case of the Newtonian fluid, a tornado-like flow that was a combination of primary and secondary circulation flows was observed with small-scale turbulent eddies. This flow required a moderate torque power and shortened the mixing time. Conversely, a large-scale primary circulation flow of a slow rigid vortex with no small-scale turbulent eddies was observed in the viscoelastic fluid. Although the discharge flow was enhanced or diminished dependently on the Reynolds number and surfactant concentration, it induced slow large-scale secondary circulation flows in the stirred vessel. As a result, the tornado-like flow disappeared, and these flows resulted in a long time constant of the mixing. Even with such flow characteristics, while the low-concentration case indicates that a low torque corresponding to the driving power is needed to drive the flow, the high-concentration case suggests that the high torque is due to the occurrence of additional viscoelastic stress.

### Effect of the streamwise pulsed arc discharge array on shock wave/boundary layer interaction control

The streamwise pulsed arc discharge array (S-PADA), in which five actuators are connected in series with adjustable frequency, is employed to control the shock wave/boundary layer interaction (SWBLI) at a 24° compression ramp in a M = 2.0 flow and under two Reynolds numbers based on boundary layer thickness (Re1 = 46 800 and Re2 = 11 700). High-speed schlieren imaging at 50 000 fps is used for flow visualization. The schlieren snapshots, as well as the statistics of the image sequence, namely, mean and root-mean-square, are examined to reveal the control outcome. The results show that the separated wave foot gradually presents bifurcation and partial disappearance under Re1 with the increasing pulse number of the S-PADA, indicating the decline in the shock intensity. The increase in frequency does affect the control outcome remarkably because shock weakening effect can be achieved under Re1 through 10 kHz and 20 kHz actuations, while no obvious change can be observed by the 5 kHz actuation. The experiments under Re2, where little control effect is exerted by the same methods, are also discussed. It is believed that the separated wave under a lower Reynolds number of Re2 presents the poorly developed turbulent boundary layer; hence, the effective SWBLI control is difficult to be ensured.

### Numerical simulation and modeling of the hydrodynamic forces and torque acting on individual oblate spheroids

Computation of a three-dimensional uniform, steady Newtonian flow past oblate spheroidal particles is undertaken. The main objective of the present study is to compute the hydrodynamic forces on oblate spheroidal particles as a function of the particle orientation, for different particle aspect ratios and a large range of particle Reynolds number. The results of the simulations are used to provide a new complete set of correlations for drag, lift, and torque coefficients. These correlations are derived for an aspect ratio ranging from 0.2 to 1, for particle Reynolds number up to 100, and for all orientations. In addition, it is found that the Stokesian evolution of the drag and lift coefficients as a function of the incidence remains still valid at moderate particle Reynolds number; that is, drag coefficient evolves as sine squared and lift coefficient evolves as (sin ϕ cos ϕ).

### On fluid flow and heat transfer of turbulent boundary layer of pseudoplastic fluids on a semi-infinite plate

The boundary layer of a pseudoplastic fluid on a semi-infinite plate for a high generalized Reynolds number is analyzed. Based on the Prandtl mixing length theory, the turbulent region is divided into two regions. The coupled momentum and temperature equations, with a generalized thermal conductivity model, have made the process of finding the analytical solutions much difficult. By using the similarity transformation, the equations are converted to four ordinary differential equations constrained by ten boundary conditions. An interesting technique of scaling and translation of the calculation domain of one region into another is used to make the system of equations easier to solve. It is found that the fluid with a smaller power-law index, associated with a thinner velocity boundary layer thickness, processes a lower friction coefficient. Furthermore, the increase in the Reynolds number causes a thinner velocity boundary layer and a decreasing friction coefficient on the wall. Changes in temperature occur more slowly near the plate surface with a rise in the power-law index and a decrease in the Reynolds number.

### Short cylindrical nozzles in a jet-driven Helmholtz oscillator

The present paper elaborates on the experimental study of jet-excited pressure fluctuations in a Helmholtz oscillator model with two openings in a cylindrical cavity. The length of the cylindrical nozzle in the front cover ℓN normalized by the nozzle diameter dN was ℓN/dN = 0.125, 0.33, 0.47, and 0.67. The diameter of the outlet opening in the back cover dOUT was in the range dOUT/dN = 1–2.5. The length of the cylindrical cavity LCH determined the jet length LJET in the spacing between the covers, LCH/dN = 0.5–3.5. The amplitude–frequency spectra were studied when the oscillator configuration was changed in the indicated intervals. From the generation amplitude, the best ratio of the sizes of the nozzle, chamber, and outlet was determined. The appearance of the jet tone of the hole and the alternation of acoustic modes were observed with a smooth increase in the Reynolds number to ∼8 · 104. The measurements showed very high amplitude of pressure fluctuations in an oscillator with a short nozzle and a short chamber at a significant jet velocity. A slight increase in the length of the chamber led to a rapid decrease in the generation amplitude. It is determined that the tone frequency is usually much lower than the resonance frequency in the chamber. Moreover, the tone frequency gradually increases with increasing jet velocity, while the resonance frequency remains unchanged, close to the natural frequency of the cavity chamber.

### Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence

Persistence is defined as the probability that the local value of a fluctuating field remains at a particular state for a certain amount of time, before being switched to another state. The concept of persistence has been found to have many diverse practical applications, ranging from non-equilibrium statistical mechanics to financial dynamics to distribution of time scales in turbulent flows and many more. In this study, we carry out a detailed analysis of the statistical characteristics of the persistence probability density functions (PDFs) of velocity and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset. Our results demonstrate that for the time scales smaller than the integral scales, the persistence PDFs of turbulent velocity and temperature fluctuations display a clear power-law behavior, associated with a self-similar eddy cascading mechanism. Moreover, we also show that the effects of non-Gaussian temperature fluctuations act only at those scales that are larger than the integral scales, where the persistence PDFs deviate from the power-law and drop exponentially. Furthermore, the mean time scales of the negative temperature fluctuation events persisting longer than the integral scales are found to be approximately equal to twice the integral scale in highly convective conditions. However, with stability, this mean time scale gradually decreases to almost being equal to the integral scale in the near-neutral conditions. Contrarily, for the long positive temperature fluctuation events, the mean time scales remain roughly equal to the integral scales, irrespective of stability.

### Shock-tube measurements of coupled vibration–dissociation time-histories and rate parameters in oxygen and argon mixtures from 5000 K to 10 000 K

Shock-tube experiments were conducted behind reflected shocks using ultraviolet (UV) laser absorption to measure coupled vibration–dissociation (CVDV) time-histories and rate parameters in dilute mixtures of oxygen (O2) and argon (Ar). Experiments probed 2% and 5% O2 in Ar mixtures for initial post-reflected-shock conditions from 5000 K to 10 000 K and 0.04 atm to 0.45 atm. A tunable, pulsed UV laser absorption diagnostic measured absorbance time-histories from the fourth, fifth, and sixth vibrational levels of the electronic ground state of O2, and experiments were repeated—with closely matched temperature and pressure conditions—to probe absorbance time-histories corresponding to each vibrational level. The absorbance ratio from two vibrational levels, interpreted via an experimentally validated spectroscopic model, determined vibrational temperature time-histories. In contrast, the absorbance involving a single vibrational level determined vibrational-state-specific number density time-histories. These temperature and state-specific number density time-histories agree reasonably well with state-to-state modeling at low temperatures but deviate significantly at high temperatures. Further analysis of the vibrational temperature and number density time-histories isolated coupling parameters from the Marrone and Treanor CVDV model, including vibrational relaxation time (τ), average vibrational energy loss (ε), vibrational coupling factor (Z), and dissociation rate constant (kd). The results for τ and kd are consistent with previous results, exhibit low scatter, and—in the case of vibrational relaxation time—extend measurements to higher temperatures than previous experiments. The results for ε and Z overlap some common models, exhibit relatively low scatter, and provide novel experimental data.