# Latest papers in fluid mechanics

### Unexpected thermo-elastic effects in liquid glycerol by mechanical deformation

It is commonly accepted that shear waves do not propagate in a liquid medium. The shear wave energy is supposed to dissipate nearly instantaneously. This statement originates from the difficulty to access “static” shear stress in macroscopic liquids. In this paper, we take a different approach. We focus on the stability of the thermal equilibrium while the liquid (glycerol) is submitted to a sudden shear strain at sub-millimeter scale. The thermal response of the deformed liquid is unveiled. The liquid exhibits simultaneous and opposite bands up to about +0.04 to −0.04 °C temperature variation, while keeping the global thermal balance unchanged. The sudden thermal changes and the long thermal relaxation highlight the ability of the liquid to convert the step strain energy in non-uniform thermodynamic states. The thermal effects depend nearly linearly on the amplitude of the deformation supporting the hypothesis of a shear wave propagation (elastic correlations) extending up to several hundreds micrometers. This new physical effect can be explained in terms of the underlying phonon physics of confined liquids, which unveils a hidden solid-like response with many similarities to glassy systems.

### Improvement of the free-interaction theory for shock wave/turbulent boundary layer interactions

Free-interaction theory is widely used for the analysis and modeling of the flow structure for shock wave/turbulent boundary layer interactions (SWTBLIs). However, many studies have demonstrated that the value of the nondimensional pressure rise function at the plateau should not be treated as a universal constant, which is an assumption taken in the traditional free-interaction theory. Such an assumption brings huge uncertainty to the theoretical prediction of shock wave/boundary layer interaction flows. To improve the accuracy of free-interaction theory, numerical simulations on the incident shock wave/turbulent boundary layer interactions are carried out in this study over an extensive flow range (Ma0 = 2.0–5.0, Reδ = 7.4 × 104–7.29 × 105). Utilizing the simulated flow field structures and literature data, this paper analyzes the essential influencing factors for determining the plateau pressure. Two nondimensional parameters—the incompressible shape factor of the incoming boundary layer and the nondimensional separation-bubble height—are identified as the essential influencing factors for the nondimensional pressure rise function at the plateau. A new scaling rule is proposed by taking these two nondimensional parameters into consideration, and the experimental data of the SWTBLIs after scaling collapse well onto a single curve with an R2 value of 0.918. The experimental data used to validate the scaling rule include incident and ramp SWTBLIs and the leading SWTBLIs in shock trains. The proposed scaling rule can be used to establish more accurate theoretical predicting models for SWTBLIs.

### A study of the internal vibration of a single oscillating bubble

A model for the compressible gas inside a single oscillating bubble is developed and found to have a wave-like distribution. Both gas sphere and ambient incompressible liquid are simplified as inviscid, ideal fluids. The density and pressure in the gas sphere are described by the Euler equations with analytical solutions obtained using the perturbation method. The zero-order quantities follow a uniform distribution. By introducing co-moving coordinates, the first-order quantities, which indicate the wave-like gas distribution, are obtained. The effect of the bubble oscillation on acoustic gas perturbations is included in our theory, and it results in a new wave equation, which describes internal wave-like distribution. According to our theory, the gas vibration induces local pressure peaks in the ambient liquid. Our theoretical description of the pressure peaks agrees with experimental observations. The observability of the internal oscillation is also discussed.

### Invited contributions from early career researchers 2020

### The wobbling motion of single and two inline bubbles rising in quiescent liquid

The wobbling motions of single and two inline bubbles rising in quiescent liquid are investigated via three-dimensional simulations using the volume of fluid method. First, we simulate an 8 mm air bubble rising in quiescent water, yielding the wobbling motion. The bubble wobbling has two roles: (1) the excessive curvature speeds up the separation of the boundary layer and (2) the velocity peaks (high Reynolds number) result in the formation of asymmetrical vortices. The oscillation frequencies (6 Hz, St = 0.22) of the bubble movement, the vorticity accumulated on the bubble surface, the lift force and viscous force are the same while the oscillation frequency of the aspect ratio is twice that of the bubble movement. The volume-averaged liquid velocity presents a linear increase with the bubble rise while the kinetic energy displays a quadratic increase. Finally, two bubbles rising inline are investigated with different initial distances. The central breakup of the trailing bubble is observed at a short distance of 2d (d is the bubble diameter). For a longer distance of 6d, the wake of the leading bubble results in the lateral motion of the trailing bubble, depending on the position of the trailing bubble in the wake and the intensity of the vortices it encounters.

### Larger wavelengths suit hydrodynamics of carangiform swimmers

Author(s): Muhammad Saif Ullah Khalid, Junshi Wang, Imran Akhtar, Haibo Dong, Moubin Liu, and Arman Hemmati

We examine the connection between the physiology and wavy kinematics of carangiform swimmers, such as Jack, Tuna, and Sunfish. Using high-fidelity numerical simulations for flows over Jack Fish models obtained through reconstruction of high-speed images of real natural swimmers, it was revealed that undulation with larger wavelengths improves the hydrodynamic performance of the carangiform swimmer in terms of better thrust production by the caudal fin, lower drag production on the trunk, and reduced power consumption by the trunk.

[Phys. Rev. Fluids 6, 073101] Published Fri Jul 09, 2021

### Learning unknown physics of non-Newtonian fluids

Author(s): Brandon Reyes, Amanda A. Howard, Paris Perdikaris, and Alexandre M. Tartakovsky

Non-Newtonian fluids have a shear-rate dependent viscosity that is difficult to measure in experiments. We present a physics-informed neural networks (PINN) approach for learning the viscosity using indirect measurements (such as velocity and pressure) subject to the momentum conservation and continuity equations constraints. We use the PINN approach to estimate viscosity of polymer melts and suspensions of particles using velocity measurements from two-dimensional shear flow simulations. The PINN-inferred viscosity models agree with empirical models for shear rates with large absolute values but deviate for shear rates near zero where the empirical models have an unphysical singularity.

[Phys. Rev. Fluids 6, 073301] Published Fri Jul 09, 2021

### Data-driven approach for noise reduction in pressure-sensitive paint data based on modal expansion and time-series data at optimally placed points

We propose a noise reduction method for unsteady pressure-sensitive paint (PSP) data based on modal expansion, the coefficients of which are determined from time-series data at optimally placed points. In this study, the proper orthogonal decomposition (POD) mode calculated from the time-series PSP data is used as a modal basis. Based on the POD modes, the points that effectively represent the features of the pressure distribution are optimally placed by the sensor optimization technique. Then, the time-dependent coefficient vector of the POD modes is determined by minimizing the difference between the time-series pressure data and the reconstructed pressure at the optimal points. Here, the coefficient vector is assumed to be a sparse vector. The advantage of the proposed method is a self-contained method, while existing methods use other data, such as pressure tap data for the reduction of the noise. As a demonstration, we applied the proposed method to the PSP data measuring the Kármán vortex street behind a square cylinder. The reconstructed pressure data agreed very well with the pressures independently measured by pressure transducers. This modal-based approach will be applicable not only to PSP data but other types of experimental data.

### Bistability bifurcation phenomenon induced by non-Newtonian fluids rheology and thermosolutal convection in Rayleigh–Bénard convection

In the present paper, a numerical investigation was performed to assess the effect of the rheological behavior of non-Newtonian fluids on Rayleigh–Bénard thermosolutal convection instabilities within shallow and finite aspect ratio enclosures. Neumann and Dirichlet thermal and solutal boundary condition types were applied on the horizontal walls of the enclosure. Using the Boussinesq approximation, the momentum, energy, and species transport equations were numerically solved using a finite difference method. Performing a nonlinear asymptotic analysis, a bistability convective phenomenon was discovered, which was induced by the combined fluid shear-thinning and aiding thermosolutal convection effects. Therefore, bistability convection was the main focus in the current study using the more practical constitutive Carreau–Yasuda viscosity model, which is valid from zero to infinite shear rates. Also, the combined effects of the rheology parameters and double diffusive bistability convection were studied. For aiding flow, the shear-thinning and the slower diffusing solute effects were counteracting and, as a result, two steady-state finite amplitude solutions were found to exist for the same values of the governing parameters, which indicated and demonstrated evidence for the existence of bistability convective flows. For opposing flows, the shear-thinning effect strengthened subcritical flows, which sustained well below the threshold of Newtonian thermosolutal convection. Thus, bistability convection did not exist for opposing flows, as both the shear-thinning and the slower diffusing component effects favored subcritical convection.

### Performance comparison among the variants of curved serpentine coil

In the present work, two variants of the novel curved serpentine coil formed by relaxing the switching angle at the junctions are explored and compared with the original design for the same mean radius Rm of concentric tubes. With α as the semi-cone angle and θ as the subtended angle of concentric tubes, the general notation given to different variants of the curved serpentine coil is CS-α-θ. The three variants are named as a cylindrical curved serpentine coil (α = 0°), conical curved serpentine coil (0° < α < 90°), and spiral curved serpentine coil (α = 90°). The fluid experiences a switching angle of 90° − α and 90° + α at the entrance and exit of every U-bend, respectively. The laminar flow of water in CS-α-θ coils (45° ≤ θ ≤ 270°, 0° ≤ α ≤ 90°) is simulated using ANSYS FLUENT version 20.2 for the range 500 ≤ Re ≤ 2000. The length-averaged Nu and f are found to decrease with an increase in either α or θ for the same mean radius Rm of concentric tubes. Secondary flow intensity is quantified using the parameter Se and is correlated with the flow and geometric parameters. Generalized correlations for predicting the average Nusselt number and friction factor for CS-α-θ coils are expressed as the sum of corresponding straight tube values and as a function of Se with a maximum deviation of ±8.5% and ±7%, respectively.

### A modified Oldroyd-B model for non-colloidal suspensions

Professor R. Byron Bird used Oldroyd models of rheological behavior over a span of around 50 years. In this paper, it is suggested that a modified Oldroyd-B model can also be used to describe the rheology of non-colloidal suspensions that have a viscoelastic matrix.

### Outflow boundary condition of multiphase microfluidic flow based on phase ratio equation in lattice Boltzmann method

This article proposes a new outflow boundary condition for the color gradient model in the multiphase lattice Boltzmann method. The boundary condition is based on the phase ratio equation and made use of the Zou–He boundary condition in single-phase flow. The boundary condition is provided in two-dimension-nine-velocity (D2Q9) and three-dimension-twenty-seven-velocity (D3Q27) schemes, for which an extension of the Zou–He boundary condition to D3Q27 is also derived and its correctness verified. Application cases, including two-phase parallel flows, droplet flows, T-junction flows, three-phase Janus droplet flows in two-dimensional (2D), and three-dimensional (3D) spaces, demonstrate the effectiveness of this new boundary condition, and the performance of a test case shows its improved pressure stability and mass conservation characteristics.

### Severe slug flow-induced nonlinear dynamic behavior of a flexible catenary riser

An experiment is conducted in a small-scale air–water test loop to investigate the severe slug flow-induced vibration of a flexible catenary riser of aspect ratio (the riser length over its internal diameter) 200. The vibration displacement of the catenary riser as well as the internal flow features is simultaneously captured by high-speed cameras. Three stages are observed during a cycle of severe slugging in the riser, including the slug formation, gas blowout, and transition stages. The spatial-temporal dynamic behavior of the flexible catenary riser is closely related to the stage of severe slug flow, liquid slug length, and liquid inventory along the riser, presenting a resonance between the oscillation and the fluid pressure fluctuation.

### Treatment of unphysical numerical oscillations via local grid refinement

Unphysical numerical oscillations (UNOs) arise when a non-dissipative scheme is employed to discretize fluid equations on a coarse grid. Treating UNOs often relies on upwind schemes, digital filtration, artificial viscosity, or adaptive mesh refinement, which are either too dissipative or too costly. We propose an alternative solution by refining one grid in regions where the flow velocity changes drastically. The effectiveness of our single-point grid refinement strategy is tested in various two-dimensional and three-dimensional flows at both laminar and turbulent flow conditions, and the results are highly favorable.

### Universal flapping states of elastic fibers in modulated turbulence

We study the fully coupled dynamics between a fully developed turbulent flow and an ensemble of immersed flexible fibers. We vary the concentration of the suspension, the mechanical properties, and the length of the fibers in a vast parametric range. For all configurations, the fiber dynamics falls in only two possible dynamical states: (i) the fiber manifests its natural response to the flow forcing or (ii) its motion fully synchronizes to the hydrodynamic timescales of the turbulent flow. This scenario holds for both a dilute condition, where the carrier flow is not affected by the fluid–structure interaction, as well as in the case where the flow is substantially altered by the presence of immersed objects. Such a backreaction effect can be macroscopically modeled in terms of the mass fraction of the suspension. Our results can be readily extended to any elastic objects interacting with fluid turbulence.

### Experimental and numerical evidence of intensified non-linearity at the microscale: The lipid coated acoustic bubble

A lipid coated bubble (LCB) oscillator is a very interesting non-smooth oscillator with many important applications ranging from industry and chemistry to medicine. However, due to the complex behavior of the coating intermixed with the nonlinear behavior of the bubble itself, the dynamics of the LCB are not well understood. In this work, lipid coated Definity® microbubbles (MBs) were sonicated with 25 MHz 30 cycle pulses with pressure amplitudes between 70 and 300 kPa. Here, we report higher order subharmonics in the scattered signals of single MBs at low-amplitude high-frequency ultrasound excitations. Experimental observations reveal the generation of period 2, period 3, and two different period 4 oscillations at low excitation amplitudes. Despite the reduced damping of the uncoated bubble system, such enhanced nonlinear oscillations have not been observed and cannot be theoretically explained for the uncoated bubble. To investigate the mechanism of the enhanced non-linearity, the bifurcation structure of the lipid coated MBs is studied for a wide range of MBs sizes and shell parameters. Consistent with the experimental results, we show that this unique oscillator can exhibit chaotic oscillations and higher order subharmonics at excitation amplitudes considerably below those predicted by the uncoated oscillator. Buckling or rupture of the shell and the dynamic variation of the shell elasticity cause the intensified non-linearity at low excitation pressure amplitudes. The simulated scattered pressure by single MBs is in good agreement with the experimental signals.

### Efficiency of pulsed-jet propulsion via thrust-drag decomposition

By using an axisymmetric immersed-boundary model, fluid dynamics of a cephalopod-inspired propeller undergoing periodic inflation–deflation deformation in background flow is numerically studied in a low Reynolds number regime. A thrust-drag decoupling method based on physical analysis is proposed, in which the jet-related thrust is obtained as the summation of three parts: the jet momentum flux, the normal stress at the exit plane, and the flow acceleration inside the body. This method enables the calculation of the propulsive efficiency, especially the efficiency at the steady-swimming state. Systematic simulations are then conducted to study the effects of the Reynolds number and stroke ratio on force generation and efficiency. Two Reynolds numbers, the incoming-flow Reynolds number [math] and the jet-flow Reynolds number Rej, are involved. When [math] is fixed, the thrust generation is found to depend mostly on jet-flow velocity at high Rej, while the effect of incoming-flow velocity is pronounced at relatively low Rej, mostly through its influence on the excessive pressure at the nozzle. Within the range of incoming-flow Reynolds number considered in this study (40–150), our results show that the whole-cycle propulsive efficiency of the propeller lies in the range of 11%–30%.

### Propeller–duct interaction on the wake dynamics of a ducted propeller

The propeller–duct interaction on the wake dynamics of a ducted propeller is numerically investigated via detached eddy simulations. The blade–blade interference and blade–duct interaction are analyzed through different configurations under non-ducted and ducted conditions. It is found that the blade–blade interference benefits the loading stability, and the duct leads to a faster efficiency decrease in a single blade with the increasing blade number. The short-wave instability dominates the wake as the unstable secondary vortices accelerates the vortex evolution. The multi-induction effect stabilizes the two tip vortices system in a two-bladed configuration, while the tip vortex grouping occurs early in a four-bladed propeller due to the combined effect of the duct retardation and smaller spiral-to-spiral distance. Additionally, the enhanced wake instability leads to the fast decline of the power spectral density peaks of kinetic energy at blade passing frequency and shaft frequency harmonics toward the far field under ducted conditions.

### Effect of torsional spring and shape on the performance of bioinspired caudal fin

The swimming ability of fish is greatly influenced by the hydrodynamics of their caudal fins. In this paper, the effects of flexibility and shape on the performance of a bioinspired panel are numerically studied. The flexibility is simplified as a torsional spring, and three typical shapes (i.e., square, convex, and concave shapes) are considered. The results are obtained based on three-dimensional numerical simulations of flapping panels at Re = 1000 and St = 0.5. It is shown that the flexibility can significantly affect the performance of pitching panels, by changing the phase lag between the motions of the fore and hind parts. When the phase lag is in the range of 0.1π–0.6π, the performance improvement can be obtained by the flexible panels, as compared with the rigid panel. Moreover, the maximum thrust (or efficiency) can be achieved by a flexible panel when the phase lag is approximately 0.35π (or 0.24π). On the other hand, it is found that the convex shape is optimal for thrust generation, but the square shape is optimal for propulsive efficiency. Moreover, the mechanism by which flexibility and shape can influence the performance of the pitching panel is analyzed. The results obtained here may provide some light on designing the efficient propulsor for microunderwater robots.

### Unsteady dynamics of a classical particle-wave entity

Author(s): Rahil N. Valani, Anja C. Slim, David M. Paganin, Tapio P. Simula, and Theodore Vo

A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional theoretical pilot-wave model with a generalized wave form, we in...

[Phys. Rev. E 104, 015106] Published Thu Jul 08, 2021