Journal Of Fluid Mechanics Research Articles

Influence of Time-Varying Freestream Conditions on the Dynamics of Unsteady Boundary-Layer Separation

Unsteady flow separation of a turbulent boundary layer under dynamic pressure gradients is investigated using the Large-Eddy Simulation technique. The unsteadiness is introduced by prescribing an oscillating freestream vertical-velocity profile at the top boundary of the domain. Although previous studies, including Ambrogi et al. (Journal of Fluid Mechanics, Vol. 945, Aug. 2022, p. A10) and Ambrogi et al. (Journal of Fluid Mechanics, Vol. 972, Oct. 2023, p. A36), focused on the kinematics of the flow and the effects of the oscillation frequency on flow separation, the goal of this paper is to analyze the effects of three time-varying freestream-forcing profiles while the oscillation frequency is kept the same for all Cases. Whereas in Case A the freestream-velocity profile changes from suction–blowing to blowing–suction in a complete cycle, Cases B and C are both suction–blowing only and the strength of the adverse pressure gradient is modulated in time. Moreover, the boundary layer in Case B never approaches a zero-pressure gradient condition. A closed separation bubble is formed for all Cases; however, its dimensions change depending on the far-field forcing. The time evolution of turbulent kinetic energy (TKE) reveals an advection mechanism of turbulent structures out of the domain for all Cases. Whereas in Case A and C the high-TKE region, generated in the separated shear layer, is washed out of the domain as a rigid body, in Case B the separation bubble remains present and the advection mechanism of TKE is characterized by a breathing pattern.

Calculation of the velocities induced by the trailing vorticity in the rotor plane of a horizontal-axis turbine or propeller

Lifting line (LL) analysis of propellers and horizontal-axis turbines requires the axial and circumferential velocities induced by the vortex system representing the blades and the trailing vorticity. If the blades are straight and radial, the induced velocities along the LLs are due only to the trailing vorticity. Accurate two-term approximations for these velocities have been developed from the exact Kawada–Hardin (KH) equations for the velocity field of a doubly infinite helical vortex of constant pitch and radius, Wood et al. (Ocean Engineering, 2021, 235). This paper describes a straightforward extension of the approximations to give the induced velocities anywhere in the equivalent of the rotor plane for a doubly infinite helix. The third term in the approximation of the KH equations is derived and compared to an alternative third term due to Okulov (Journal of Fluid Mechanics, 2004, 521, 319–342). Both three-term approximations produce a small improvement in accuracy over the two-term approximations for a range of operating conditions for turbines and propellers. Okulov’s third term is superior. To determine the induced velocities for a singly infinite trailing vortex behind a rotor, an additional equation is derived from the Biot–Savart law. Numerical examples show that the resulting equations provide accurate estimates for the induced velocities over the rotor plane. The main application of the analysis is to account for blade sweep and coning by including the angle between the vortex origin and the control point at which the velocities are required, often the center of each blade element.

Wall-Modeled Large-Eddy Simulation of Turbulent Boundary Layer with Spatially Varying Pressure Gradients

Wall-modeled large-eddy simulations of turbulent boundary layers subjected to spatially varying streamwise pressure gradients are conducted to assess the predictive performance of three wall models: ordinary differential equation equilibrium, integral nonequilibrium, and partial differential equation (PDE) nonequilibrium models. The test case is based on experiments conducted by Volino (Journal of Fluid Mechanics, Vol. 897, Aug. 2020, p. A2), where the flow is subjected successively to zero pressure gradient (ZPG), favorable pressure gradient (FPG), recovery ZPG, and adverse pressure gradient (APG) regions. Skin friction is overpredicted in FPG by all the wall models. For equilibrium and integral models, this overprediction is attributed to the strong deviation of mean velocity profiles within FPG from the log law, used explicitly in the equilibrium and implicitly in the integral model. The overprediction is more pronounced for the PDE model, which is attributed to dynamic correction of wall-model eddy viscosity for resolved stresses and a lack of correction for pressure gradient. Potential remedies to mitigate this problem are proposed. Grid refinement improves wall-stress predictions in both FPG and APG but only affects the outer profiles in APG, revealing that accurate wall-flux modeling is more critical for APG. Anisotropic grid analysis shows streamwise grid refinement to be more crucial than spanwise for the convergence of skin-friction, outer velocity, and Reynolds stress profiles.

Effects of non-isotropic blockage on a tidal turbine modeled with the Actuator-Line method

Blockage effects are a consequence of the interaction between a body and the surrounding boundaries in a constrained flow. For the case of tidal rotors, global blockage (β) is usually defined bythe ratio between the swept area of the rotor and the cross-sectional area of a channel. Increasingblockage tends to increase the limits of power extraction (Garrett and Cummins, 2007), as well asthrust on a rotor through an attendant increase of through-rotor mass flow. While these observations have been studied and demonstrated for isotropic blockage effects (e.g., Zilic de Arcos et al.2020, Bahaj 2007 , Mikkelsen 2002), questions remain regarding the validity of such assumptionsfor non-isotropic blockage in channels with, e.g., rectangular cross-sections with varying aspectratios.
 In this work, we will use CFD simulations to analyze the effect of non-isotropic blockage on atidal rotor. The study aims to explore these effects using an Actuator-Line representation of anaxial-flow rotor, simulated under different blockage ratios (1 %, 5 %, 10%, and 19.7 %), aspectratios (0.25, 0.5, 0.75, and 1), and tip speed ratios (4, 5, 6, and 7). A total of 64 cases will beconsidered. For each simulated case, the power, thrust, and spanwise force distributions will beextracted as functions of time, and used to understand the effect of blockage on the performanceof tidal rotors.
 Our preliminary results, in agreement with existing literature, indicate that blockage affectswake development, as seen in Figure , along with power and thrust. These results, for a constantaspect ratio, show power increases up to 26 % for a blockage of 20 %. The bulk of the simulationmatrix, including the different aspect ratios, is currently under production and is expected to beready before the paper submission deadline.
 
 ReferencesGarrett, C., Cummins, P. (2007). The efficiency of a turbine in a tidal channel. Journal of fluidmechanics, 588, 243-251.Zilic de Arcos, F., Tampier, G., Vogel, C. R. (2020). Numerical analysis of blockage correctionmethods for tidal turbines. Journal of Ocean Engineering and Marine Energy, 6, 183-197Bahaj, A. S., Molland, A. F., Chaplin, J. R., Batten, W. M. J. (2007). Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitationtunnel and a towing tank. Renewable energy, 32(3), 407-426.Mikkelsen, R., Sørensen, J. N. (2002). Modelling of wind turbine blockage. In 15th IEAsymposium on the aerodynamics of wind turbines, FOI Swedish Defence Research Agency.
 

The capillary pressure curves from upscaling interfacial and unsaturated flows in porous layers with vertical heterogeneity

We provide the capillary pressure curves pc(s¯) as a function of the effective saturation s¯ based on the theoretical framework of upscaling unsaturated flows in vertically heterogeneous porous layers proposed recently (Z. Zheng, Journal of Fluid Mechanics, 950, A17, 2022). Based on the assumption of vertical gravitational-capillary equilibrium, the saturation distribution and profile shape of the invading fluid can be obtained by solving a nonlinear integral-differential equation. The capillary pressure curves pc(s¯) can then be constructed by systematically varying the injection rate. Together with the relative permeability curves k¯rn(s¯) that are already obtained. One can now provide quick estimates on the overall behaviours of interfacial and unsaturated flows in vertically-heterogeneous porous layers.

Lie group analysis of flow and heat transfer of a nanofluid in cone–disk systems with Hall current and radiative heat flux

A study of the rheological and heat transport characteristics in cone–disk systems finds relevance in many applications such as viscometry, conical diffusers, and medical devices. Therefore, a three‐dimensional axisymmetric flow with heat transport of a magnetized nanofluid in a cone–disk system subjected to Hall current and thermal radiation effects is investigated. The simplified Navier–Stokes (NS) equations for the cone–disk system given by Sdougos et al. [18] Journal of Fluid Mechanics, 138, 379–404 are solved by using the asymptotic expansion method for the four different models, such as rotating cone with static disk (Model I), rotating disk with static cone (Model II), co‐rotating cone and disk (Model III), and counter‐rotating cone and disk (Model IV). The Khanafer–Vafai–Lightstone (KVL) model along with experimental data‐based properties of 37 nm Al2O3–H2O nanofluid is considered. To obtain the transformations leading to self‐similar equations from the Navier–Stokes (NS) and energy conservation equations, the Lie group technique is used. The self‐similar nonlinear problem is solved numerically to examine the effects of physical parameters. There are critical values of the power exponent at which no heat transport from the disk surface occurs. Nanoparticles significantly enhance heat transport when both the cone and disk rotate in the same or opposite directions. The centrifugal force and thermal radiation improve the heat transport in cone–disk systems.

Empirical Closure Model for Coupling Mode Prediction in Supersonic Rectangular Twin Jets

An empirical closure model of rectangular twin jets’ screech and coupling has been developed to predict their coupling mode at a given flow condition. It builds on Powell’s original screech closure model (Powell, A., “On the Mechanism of Choked Jet Noise,” Proceedings of the Physical Society, Section B, Vol. 66, No. 12, 1953, pp. 1039–1056) of feedback waves produced by the interactions of large-scale structures (LSSs) with each shock cell. Powell’s work is expanded to include nonuniform shock-cell spacing, overexpanded flow regimes, and twin jet configurations. The feedback wave interference pattern strength at the nozzle exit is postulated to determine the realized coupling mode. The required empirical parameters are the shock-cell streamwise locations and the convective velocity of the LSSs. The model was validated using data from an experimental investigation of rectangular twin jets at overexpanded and underexpanded conditions. The coupling mode is correctly predicted for 11 of the 12 nozzle pressure ratios tested. Two datasets from the literature (Jeun et al., “Aeroacoustics of Twin Rectangular Jets Including Screech: Large-Eddy Simulations with Experimental Validation,” AIAA Journal, Vol. 60, No. 11, 2022, pp. 1–21 and Raman, G., and Taghavi, R., “Coupling of Twin Rectangular Supersonic Jets,” Journal of Fluid Mechanics, Vol. 354, Jan. 1998, pp. 123–146) were also examined, and the model made accurate predictions of the coupling mode for all seven reported cases. The response of the twin jets to flow control at various artificially imposed frequencies and excitation modes strongly supports the model predictions, highlighting their usefulness as a guide for the implementation of active flow control in twin jets.

Robustness of Reduced-Order Jet Noise Models

Three statistical jet noise prediction models are compared for a representative set of single-stream jet cases, which include cold and hot jets of the Strategic Investment in Low-Carbon Engine Technology experiment at an acoustic Mach number of 0.875 as well as the cold jets of the NASA small hot jet acoustic rig experiment at acoustic Mach numbers of 0.5 and 0.9. The implemented models are those proposed by Tam and Auriault (Jet Mixing Noise from Fine-Scale Turbulence,” AIAA Journal, Vol. 37, No. 2, 1999, pp. 145–153), Khavaran and Bridges (“An Empirical Temperature Variance Source Model in Heated Jets,” NASA TM 2012-217743, 2012), and the Goldstein’s “A Generalized Acoustic Analogy,” Journal of Fluid Mechanics, Vol. 488, July 2003, pp. 315–333) generalized acoustic analogy (GAA) model. By virtue of reduced-order modeling, which is based on the single-point mean flow and turbulence statistics, all of these implementations use a number of empirical dimensionless source parameters for far-field noise spectra predictions. In comparison with the Tam and Auriault model, the Khavaran and GAA model implementations use several dimensionless parameters, which are available from previous literature and assumed to be more or less universal for a class of single-stream jets. These parameters include the fluctuating enthalpy function and the dimensionless amplitudes of autocovariances of turbulent fluctuating stresses and velocities available from the literature. The comparison of the three models is aimed at not only assessing their accuracy for a range of jet conditions, observer angles, and frequencies but also to examine their robustness outside of a reference jet experiment for which their source models were calibrated. For the input to each model, the mean flow, turbulence kinetic energy, and dissipation rate extracted from Large Eddy Simulations and Reynolds-averaged Navier–Stokes solutions are considered.

Effects of Wall Temperature on Hypersonic Impinging Shock-Wave/Turbulent-Boundary-Layer Interactions

We carry out a parametric study of hypersonic impinging shock-wave/turbulent-boundary-layer interactions (SBLIs) at hypersonic conditions (Mach number 6.0) by means of numerical simulation of the Reynolds-averaged Navier–Stokes (RANS) equations, with the eventual goal of establishing wall temperature and Reynolds number effects. Comparison with available direct numerical simulation and experimental data shows that RANS is capable of predicting the main features of SBLI, namely, typical size and distribution of the wall properties. A large number of flow cases were computed to examine the scaling of the global flow parameters over a wide range of wall temperatures and Reynolds numbers. As expected, the interaction zone is reduced as the wall is cooled, and as the Reynolds number is increased. A modified form of the scaling originally introduced by Souverein et al. [Journal of Fluid Mechanics, Vol. 714, 2013, pp. 505–535] is here considered to account for nonadiabatic wall state, which is found to successfully collapse the data to the distributions obtained for adiabatic flow, with some remaining deviations associated with low-Reynolds-number effects.

Comparative Additional Factor for Diffraction Loss On (TEM01) Mode from That of (TEM00) Mode

Comparative Additional Factor for Diffraction Loss On (TEM01) Mode from That of (TEM00) Mode

Scaling Laws for Three-Dimensional Combined Heaving and Pitching Propulsors

We present three-dimensional scaling relations for the thrust production and power consumption of combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (“Scaling Laws for the Propulsive Performance of Three-Dimensional Pitching Propulsors,” Journal of Fluid Mechanics, Vol. 871, July 2019, pp. 1117–1138). Self-propelled inviscid simulations and previously published experimental data are used to validate the scaling laws over a wide range of motion amplitudes, Strouhal numbers, heave ratios, aspect ratios, and pitch axis locations. The scaling laws are shown to predict inviscid numerical and experimental data well, within and of the thrust and power data, respectively. It reveals that both the circulatory and added mass forces are important when considering a wide range of motion amplitudes and that nonlinear corrections to the classic linear theory are essential to modeling the power performance across a wide amplitude and aspect ratio range. By using the scaling laws as a tool, it is obtained that peak efficiency occurs when dimensionless amplitude and for these large-amplitude motions there is an optimal nondimensional heave ratio , where the efficiency maximizes in the narrow range of . Finally, the scaling laws show that to further improve efficiency in this high-efficiency regime, the aspect ratio and dimensionless amplitude should be increased, whereas the Lighthill number should be decreased (lower drag and/or a larger propulsor planform area to wetted surface area ratio), and the pitch axis should be located behind the leading edge. This scaling model can be used to guide the design of the next generation of high-efficiency bio-inspired machines.

Reformulation and improvement of a universal subgrid eddy viscosity model based on the multiscale framework

A universal multiscale Smagorinsky model (UMSM) is established for the large eddy simulation (LES) of wall-bounded turbulent flows by reformulating a universal subgrid eddy viscosity model presented by Gu et al. (Europhysics Letter 94(3):34003,2011). The UMSM is adapted to the LES of wall-bounded turbulent flows by integrating the “small-all” form of the multiscale Smagorinsky model with the dynamic subgrid characteristic length, controlled by subgrid-scale (SGS) motions. The dynamic subgrid characteristic length is determined by the characteristic wave number, which is calculated from a new energy-weighted-mean method when the SGS turbulent kinetic energy and the dissipation wave number are known. The dissipation wave number is derived from the SGS turbulent kinetic energy spectrum equation and the total dissipation rate spectrum equation. The UMSM is used to simulate the fully developed channel flow and the turbulent flow past a square cylinder. The dynamic subgrid characteristic length, as a counterpart of Germano’s procedure, evaluates the rapidly fluctuating small-scale behavior and spatial variations of turbulent characteristics. The results for fully developed channel flow show that the errors in the streamwise velocity and the velocity fluctuations change slowly. The flat nature of the UMSM error across different multiscale Smagorinsky coefficients (Cs’) indicates that the model is relatively insensitive to the value of Cs′. Additionally, the UMSM is less sensitive to grid resolution since more details of turbulence fluctuations are captured on the same grid-points compared to the RVBMM (Journal of Computational Physics, 234:79-107,2013) and DSM (Journal of Fluid Mechanics 319:353-385,1996). Overall, the proposed model and the DSM exhibit similar behavior, and both LES formulations provide good agreement with reference data from direct numerical simulations. However, the UMSM is more computationally efficient, being 17% faster than the dynamic Smagorinsky model.

Pressure propagation and flow restart in a pipeline filled with a gas pocket separated rheomalaxis elasto-viscoplastic waxy gel

A clogged waxy crude oil pipeline, entails a high pressure to de-structure the gelled oil and resume its normal operation. Our earlier work, which utilized generalized Newtonian fluid based model, demonstrated that the presence of a gas pocket in-between the gel plugs, delays pressure propagation in the downstream gel plug [L. Tikariha, L. Kumar, Pressure propagation and flow restart in the multi-plug gelled pipeline, Journal of Fluid Mechanics. 911 (2021)]. This delay in pressure propagation is effectively utilized for sequential gel degradation. In the present work, we consider gel as a rheomalaxis elasto-viscoplastic (REVP) fluid, capable in predicting flow stoppage and pressure signal stoppage. The governing equations for mass, momentum balance, and phase equation are solved together with the REVP rheology model. The propagation of pressure in a REVP gel-filled pipeline is directly related to the gel material's elastic response. For a REVP gel, the flow-restart in a gelled pipeline depends on the conditional statement γ>γs (i.e. mean gel deformation overcoming the yield strain). In the case of a single gel plug, no-pressure propagation is predicted at intermediate compressibility, whereas pressure propagation without flow restart is predicted at low compressibility. In these cases, the presence of a small gas pocket instigates the gel breakage process, resulting in a flow restart. The gas pocket delays the pressure propagation in the second gel plug, resulting in a pressure gradient higher than yield stress across the first gel plug. The first gel plug, which deforms under a high-pressure gradient, compresses the gas pocket. This results in a larger mean deformation in the first gel plug, and it overcomes the threshold yield strain limit (γs). At strain values larger than yield strain the gel structure breaks, resulting in a lower elastic strength in the first gel plug. The lower elastic gel strength ascertains a lower pressure gradient in the first gel plug, allowing a largely unattenuated pressure to propagate in the second plug. The propagation of unattenuated pressure in the second gel plug results in a pressure gradient higher than the yield stress. This causes sequential gel breakage, resulting in a successful flow restart in a pipeline longer than a critical length. The present study also demonstrates that the pressure propagation and initial transient flow depend on the gel properties (i.e. gel strength and compressibility) and the number and size of gas pockets in the gel. The insights gained from the present work provide a cost-effective solution to mitigate the flow restart problem.

Scaling Analysis on the Dynamic and Instability Characteristics of Isolated Wingtip Vortex

The isolated wingtip vortex is generated by an M6 wing under different angles of attack and Reynolds numbers , and is measured within 16 chord length downstream regions. Then, the spatiotemporal local linear stability analysis (LSA) is performed at the azimuthal wavenumber of to analyze the instability characteristics. Experimental results show that the radial circulation of wingtip vortex satisfies a scaling formula. Moreover, the LSA results demonstrate that the instability characteristics, including the stability curve, growth rate eigenvalue spectrum, and perturbation mode, are uniformed in time and space, laying the basis for scaling the wingtip vortex by considering them. In this situation, by plotting the circulation-based Reynolds number and dimensionless wandering amplitude in log scale, it is found that they are in the form of , where and . Particularly, along with the streamwise development, the swirl number of wingtip vortex asymptotically closes to the unstable region in the (, ) plane defined by Fabre and Jacquin (Journal of Fluid Mechanics, Vol. 500, Jan. 2004, pp. 239–262). By considering the role of growth rate in the vortex wandering, an alternative scaling formula , where and , is suggested to describe the wandering development.

A Low-Communication-Overhead Parallel DNS Method for the 3D Incompressible Wall Turbulence

This paper presents a low-communication-overhead parallel method for direct numerical simulations of the 3D incompressible wall turbulence. A fully explicit projection method with second-order space-time accuracy is adopted. Combined with fast Fourier transforms, the parallel diagonal dominant (PDD) algorithm for the tridiagonal system is employed to solve the pressure Poisson equation. The number of all-to-all communications is decreased to only two, in a 2D pencil-like domain decomposition. The resulting MPI/OpenMP hybrid parallel code shows excellent strong scalability up to 104 cores and small wall-clock time per timestep. Numerical simulations of turbulent channel flow at different friction Reynolds numbers () have been conducted and the statistics are in good agreement with the reference data and the recent scaling theories [Chen, X. and K. R. Sreenivasan. 2021. “Reynolds Number Scaling of the Peak Turbulence Intensity in Wall Flows.” Journal of Fluid Mechanics 908: R3. doi:10.1017/jfm.2020.991].

Celebrating George K. Batchelor's Centenary

Abstract

Assessing Wall-Modeled Large-Eddy Simulation for Low-Speed Flows with Heat Transfer

This paper reports wall-modeled large-eddy simulation (WMLES) results of low-speed turbulent flows in a plane channel, in ribbed ducts, and around a film cooling jet. We compare our WMLESs to Pirozzoli et al.’s direct numerical simulations (DNSs) of low-speed plane channel flow (Pirozzoli, S., Bernardini, M., and Orlandi, P., “Passive Scalars in Turbulent Channel Flow at High Reynolds Number,” Journal of Fluid Mechanics, Vol. 788, Feb. 2016, pp. 614–639), our own DNSs of ribbed ducts with various pitch-to-height ratios, and Milani et al.’s WRLES and water-tunnel experiment of film cooling (Milani, P. M., Gunady, I. E., Ching, D. S., Banko, A. J., Elkins, C. J., and Eaton, J. K., “Enriching MRI Mean Flow Data of Inclined Jets in Crossflow with Large Eddy Simulations,” International Journal of Heat and Fluid Flow, Vol. 80, Dec. 2019, Paper 108472). We consider Mach number effects below the often-quoted low-Mach-number limit of . The results show that the Mach number has significant effects on the normalized mean temperature profile, even below the often-quoted low-Mach-number limit of , due to the associated viscous heating. In addition, we compare the first-grid point implementation (FGI) and the third-grid point implementation (TGI) of the equilibrium wall model. We show that, by placing the large-eddy-simulation/wall-model matching location away from the wall, TGI practically reduces the near-wall resolution seen by the wall model, which in turn leads to underperformance of the wall model. By considering three types of flows with increasing levels of complexities, the objective of this study is to systematically assess WMLES in terms of its ability to predict heat transfer for low-speed flows. For the flows considered here (that is, plane channel, ribbed duct, and film cooling), we show that WMLES with FGI is able to accurately model heat transfer at a much more reduced cost than WRLES and DNS.

Design waves and statistics of linear gap resonances in random seas

Water wave resonance between two side-by-side vessels is a multimode resonant hydrodynamic phenomenon with low damping. The potential flow damping and viscous damping inside the gap play a significant role, influencing the amplitudes of the gap resonances. The frequencies of the gap modes can be well predicted by linear potential flow theory, while much effort has been made to explore the nature of the viscous damping. A series of experiments is conducted to explore the temporal (Zhao et al., Journal of Fluid Mechanics, vol. 812, 2017, 905–939) and spatial structure (Zhao et al., Journal of Fluid Mechanics, vol. 883, 2020, A22) of the resonant responses along the gap. Ultimately, it is of practical interest to understand the response statistics along the gap in random seas, to facilitate decision making for safe offshore operations. Following our previous studies which focused on new physics, here we identify the design waves that produce the most probable maximum responses under unidirectional random linear wave excitation. This is achieved through an efficient prediction model within linear theory. Combining the experimental data and linear potential flow calculations, we provide the lower and upper bounds of gap responses, bracketing possible responses at field scale. The statistical model is expected to be of practical importance for offshore operations.

Modeling the motion of a Taylor bubble in a microchannel through a shear-thinning fluid

Applications of multiphase flows in microchannels as chemical and biological reactors and cooling systems for microelectronic devices typically present liquid slugs alternated with bubbles of elongated shape, the Taylor bubbles. These occupy almost entirely the cross-section of the channel and present a hemispherical front and a liquid layer, the lubrication film, which separates the gas from the tube wall. The Taylor bubble perturbs the surrounding fluids activating many transport mechanisms in the proximity of the gas-liquid interface; therefore, the bubble motion significantly influences the heat and mass transfer rates. Although many works deeply investigate the bubble hydrodynamics in Newtonian fluids, the knowledge about the relation between bubble hydrodynamics and rheological properties is insufficient, and studies where the continuous phase exhibits a shear-thinning behavior are missing. Our numerical analysis tries to fill this gap by investigating the motion of a Taylor bubble in a non-Newtonian shear-thinning fluid, modeled by the Carreau viscosity model. First, we validate the results against the Newtonian case and a recent theory for shear-thinning fluids (Picchi et al., Journal of Fluid Mechanics, 2021, 918). Then, we investigate the bubble hydrodynamics far from the validity range of the current models. Finally, we study the scaling of the bubble velocity and lubrication film thickness, extending the current theory to shear-thinning fluids.

Gust–Airfoil Coupling with a Loaded Airfoil

The unsteady load response of an airfoil encountering a gust is often modeled using analytical transfer functions, which assume idealized behavior of both the flow and the airfoil. One such transfer function is the Sears function, which models a pure transverse gust interacting with a flat-plate airfoil at zero mean incidence. The function was extended by Goldstein and Atassi (“A Complete Second-Order Theory for the Unsteady Flow About an Airfoil due to a Periodic Gust,” Journal of Fluid Mechanics, Vol. 74, No. 4, 1976, pp. 741–765) to account for camber and incidence, as well as the presence of a streamwise gust component. Atassi (“The Sears Problem for a Lifting Airfoil Revisited-New Results,” Journal of Fluid Mechanics, Vol. 141, April 1984, pp. 109–122) showed that the effects of camber and incidence (that is, nonzero mean airfoil loading) are not negligible when there is a streamwise gust component. In this work, new experimental data are shown for an airfoil with nonzero loading encountering a gust with both streamwise and transverse components. As well as giving validation to the Atassi model, the flow physics behind the model is shown, including the superposition of the gust onto the airfoil potential field and the propagation of the gust along the airfoil surface.