Showing papers in "Physics of Fluids in 2016"

Mean velocity scaling for compressible wall turbulence with heat transfer

Abstract: The current state-of-the-art in accounting for mean property variations in compressible turbulent wall-bounded flows is the Van Driest transformation, which is inaccurate for non-adiabatic walls. An alternative transformation is derived, based on arguments about log-layer scaling and near-wall momentum conservation. The transformation is tested on supersonic turbulent channel flows and boundary layers, and it is found to produce an excellent collapse of the mean velocity profile at different Reynolds numbers, Mach numbers, and rates of wall heat transfer. In addition, the proposed transformation mathematically derives the semi-local scaling of the wall-normal coordinate and unifies the scaling of the velocity, the Reynolds stresses, and the wall-normal coordinate.

Using field inversion to quantify functional errors in turbulence closures

Abstract: A data–informed approach is presented with the objective of quantifying errors and uncertainties in the functional forms of turbulence closure models. The approach creates modeling information from higher-fidelity simulations and experimental data. Specifically, a Bayesian formalism is adopted to infer discrepancies in the source terms of transport equations. A key enabling idea is the transformation of the functional inversion procedure (which is inherently infinite-dimensional) into a finite-dimensional problem in which the distribution of the unknown function is estimated at discrete mesh locations in the computational domain. This allows for the use of an efficient adjoint-driven inversion procedure. The output of the inversion is a full-field of discrepancy that provides hitherto inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) are used, the accuracy of the inferred solution is improved over the entire computational domain. The results suggest that, by directly addressing the connection between physical data and model discrepancies, the field inversion approach materially enhances the value of computational and experimental data for model improvement. The resulting information can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.

Input-output analysis of high-speed axisymmetric isothermal jet noise

Abstract: We use input-output analysis to predict and understand the aeroacoustics of high-speed isothermal turbulent jets. We consider axisymmetric linear perturbations about Reynolds-averaged Navier-Stokes solutions of ideally expanded turbulent jets with jet Mach numbers 0.6 < Mj < 1.8. For each base flow, we compute the optimal harmonic forcing function and the corresponding linear response using singular value decomposition of the resolvent operator. In addition to the optimal mode, input-output analysis also yields sub-optimal modes associated with smaller singular values. For supersonic jets, the optimal response closely resembles a wavepacket in both the near-field and the far-field such as those obtained by the parabolized stability equations (PSE), and this mode dominates the response. For subsonic jets, however, the singular values indicate that the contributions of sub-optimal modes to noise generation are nearly equal to that of the optimal mode, explaining why the PSE do not fully capture the far-fiel...

Turbulent drag reduction over air- and liquid- impregnated surfaces

Abstract: Results on turbulent skin friction reduction over air- and liquid-impregnated surfaces are presented for aqueous Taylor-Couette flow. The surfaces are fabricated by mechanically texturing the inner cylinder and chemically modifying the features to make them either non-wetting with respect to water (air-infused, or superhydrophobic case), or wetting with respect to an oil that is immiscible with water (liquid-infused case). The drag reduction, which remains fairly constant over the Reynolds number range tested (100 ≤ Reτ ≤ 140), is approximately 10% for the superhydrophobic surface and 14% for the best liquid-infused surface. Our results suggest that liquid-infused surfaces may enable robust drag reduction in high Reynolds number turbulent flows without the shortcomings associated with conventional superhydrophobic surfaces, namely, failure under conditions of high hydrodynamic pressure and turbulent flow fluctuations.

The Noble-Abel Stiffened-Gas equation of state

Abstract: Hyperbolic two-phase flow models have shown excellent ability for the resolution of a wide range of applications ranging from interfacial flows to fluid mixtures with several velocities. These models account for waves propagation (acoustic and convective) and consist in hyperbolic systems of partial differential equations. In this context, each phase is compressible and needs an appropriate convex equation of state (EOS). The EOS must be simple enough for intensive computations as well as boundary conditions treatment. It must also be accurate, this being challenging with respect to simplicity. In the present approach, each fluid is governed by a novel EOS named “Noble Abel stiffened gas,” this formulation being a significant improvement of the popular “Stiffened Gas (SG)” EOS. It is a combination of the so-called “Noble-Abel” and “stiffened gas” equations of state that adds repulsive effects to the SG formulation. The determination of the various thermodynamic functions and associated coefficients is the...

Self-diffusiophoretic colloidal propulsion near a solid boundary

Abstract: Self-propelled, chemically powered colloidal locomotors are swimmers designed to transverse small scale landscapes in a range of applications involving micropumping, sensing, and cargo transport. Although applications can require precise navigation and onboard steering mechanisms, here we examine by calculation how locomotors through their hydrodynamic interaction can navigate along a boundary. We adopt an engine model consisting of a spherical Janus colloid coated with a symmetrical catalyst cap, which converts fuel into a product solute. The solute is repelled from the colloid through a repulsive interaction, which occurs over a distance much smaller than the swimmer radius. Within this thin interaction layer, a concentration difference develops along the surface, which generates a pressure gradient as pressure balances the interaction force of the solute with the surface. The pressure gradient drives a slip flow towards the high concentration, which propels the particle oppositely, away from product accumulation (self-diffusiophoresis). To study boundary guidance, the motion near an infinite no-slip planar wall that does not adsorb solute is obtained by analytical solution of the solute conservation and the Stokes equations using bispherical coordinates. Several regimes of boundary interaction unfold: When the colloid is oriented with its cap axisymmetrically facing the wall, it is repelled by the accumulation of solute in the gap between the swimmer and the wall. With the cap opposite to the wall, the swimmer moves towards the wall by the repulsion from the solute accumulating on the cap side, but very large caps accumulate solute in the gap, and the motor stops. For oblique approach with the cap opposite to the wall and small cap sizes, the swimmer is driven to the wall by accumulation on the cap side, but rotates as it approaches the wall, and eventually scatters as the cap reorients and faces the wall. For a swimmer approaching obliquely with a larger cap (again facing away from the wall), boundary navigation results as the accumulation of product in the gap suppresses rotation and provides a normal force, which directs the swimmer to skim along the surface at a fixed distance and orientation or to become stationary. We also demonstrate how gravity can force transitions between skimming and stationary states.

Small-charge underwater explosion bubble experiments under various boundary conditions

Abstract: Small-charge underwater explosion experiments were performed to investigate bubbles subjected to gravity and various boundary conditions, including single boundary (free surface and rigid wall boundary), combined boundaries of free surface and solid wall, solid wall boundaries with a circular opening, and resilient wall boundaries. With high speed camera and pressure sensors, the behavior of explosion bubbles was studied and features of associated pressure pulses were analyzed. Detailed image analysis on the final stages of bubble collapse was carried out and revealed a possible explanation for the weakening of pressure waves at bubble rebound as the bubble approaches a wall boundary. Certain features also indicate that the magnitude of the pressure peaks induced by bubble rebound is related to the shape of the bubble shape during collapse. Pressure pulses arising from the two types of bubble behavior, specifically the collision of an annular jet and the impact of a jet with the wall boundary, were measur...

Simulation of bubble expansion and collapse in the vicinity of a free surface

Abstract: The present paper focuses on the numerical simulation of the interaction of laser-generated bubbles with a free surface, including comparison of the results with instances from high-speed videos of the experiment. The Volume Of Fluid method was employed for tracking liquid and gas phases while compressibility effects were introduced with appropriate equations of state for each phase. Initial conditions of the bubble pressure were estimated through the traditional Rayleigh Plesset equation. The simulated bubble expands in a non-spherically symmetric way due to the interference of the free surface, obtaining an oval shape at the maximum size. During collapse, a jet with mushroom cap is formed at the axis of symmetry with the same direction as the gravity vector, which splits the initial bubble to an agglomeration of toroidal structures. Overall, the simulation results are in agreement with the experimental images, both quantitatively and qualitatively, while pressure waves are predicted both during the expansion and the collapse of the bubble. Minor discrepancies in the jet velocity and collapse rate are found and are attributed to the thermodynamic closure of the gas inside the bubble.

Electroosmosis-modulated peristaltic transport in microfluidic channels

Abstract: We analyze the peristaltic motion of aqueous electrolytes altered by means of applied electric fields. Handling electrolytes in typical peristaltic channel material such as polyvinyl chloride and Teflon leads to the generation of a net surface charge on the channel walls, which attracts counter-ions and repels co-ions from the aqueous solution, thus leading to the formation of an electrical double layer—a region of net charges near the wall. We analyze the spatial distribution of pressure and wall shear stress for a continuous wave train and single pulse peristaltic wave in the presence of an electrical (electroosmotic) body force, which acts on the net charges in the electrical double layer. We then analyze the effect of the electroosmotic body force on the particle reflux as elucidated through the net displacement of neutrally buoyant particles in the flow as the peristaltic waves progress. The impact of combined electroosmosis and peristalsis on trapping of a fluid volume (e.g., bolus) inside the travelling wave is also discussed. The present analysis goes beyond the traditional analysis, which neglects the possibility of coupling the net pumping of fluids due to peristalsis and allows us to derive general expressions for the pressure drop and flow rate in order to set up a general framework for incorporating flow control and actuation by simultaneous peristalsis and application of electric fields to aqueous solutions. It is envisaged that the results presented here may act as a model for the design of lab-on-a-chip devices.

Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows

Abstract: In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10%–15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method’s advantages are illustrated for the simulation of a developing wind-farm boundary layer.

Flow and heat simultaneously induced by two stretchable rotating disks

Abstract: An exact solution for the steady state Navier-Stokes equations in cylindrical coordinates is presented in this work. It serves to investigate the fluid flow and heat transfer occurring between two stretchable disks rotating co-axially at constant distance apart. The governing equations of motion and energy are first transformed into a set of nonlinear differential equation system by the use of von Karman similarity transformations, which are later solved numerically. The small Reynolds number case allows us to extract closed-form solutions for the physical phenomenon. The effects of the same or opposite direction rotation, as well as the stretching parameter and the Reynolds number, are discussed on the flow and heat characteristics. The main physical implication of the results is that stretching action of a disk surface alters considerably the classical flow behavior occurring between two disks and the physically interesting quantities like the torque and heat transfer are elucidated in the presence of a new physical mechanism; that is the surface stretching in the current research.

Large-eddy simulation of nitrogen injection at trans- and supercritical conditions

Abstract: Large-eddy simulations (LESs) of cryogenic nitrogen injection into a warm environment at supercritical pressure are performed and real-gas thermodynamics models and subgrid-scale (SGS) turbulence models are evaluated. The comparison of different SGS models — the Smagorinsky model, the Vreman model, and the adaptive local deconvolution method — shows that the representation of turbulence on the resolved scales has a notable effect on the location of jet break-up, whereas the particular modeling of unresolved scales is less important for the overall mean flow field evolution. More important are the models for the fluid’s thermodynamic state. The injected fluid is either in a supercritical or in a transcritical state and undergoes a pseudo-boiling process during mixing. Such flows typically exhibit strong density gradients that delay the instability growth and can lead to a redistribution of turbulence kinetic energy from the radial to the axial flow direction. We evaluate novel volume-translation methods on the basis of the cubic Peng-Robinson equation of state in the framework of LES. At small extra computational cost, their application considerably improves the simulation results compared to the standard formulation. Furthermore, we found that the choice of inflow temperature is crucial for the reproduction of the experimental results and that heat addition within the injector can affect the mean flow field in comparison to results with an adiabatic injector.

Three-dimensional flow field over a trailing-edge serration and implications on broadband noise

Abstract: The three-dimensional flow field over the suction side of a NACA 0018 airfoil with trailing-edge serrations was studied by means of time-resolved tomographic particle image velocimetry. Mean flow results show that the boundary layer thickness decreases along the streamwise direction with a corresponding reduction of the size of the turbulent structures developing over the suction side of the serrations. At a positive angle of attack, streamwise-oriented and counter-rotating vortices aligned with the edge of the serrations are found to be the main features of the mean flow field. Their formation is attributed to the pressure imbalance between the two sides of the airfoil and the mixing layer at the edge. They locally modify the effective angle seen by the turbulent flow approaching the serrated edge. This effect may contribute to the serration underperformance in terms of noise reduction reported in literature. The spatial distribution of the spectra of the source term of the Poisson equation, which relates the velocity field to pressure fluctuations, suggests that the contribution of the serrations to far-field broadband noise is a function of the streamwise location. This observation is congruent with the spectra of the wall-normal and spanwise velocity fluctuations, which typically show low intensity close to the tips of the individual serrations. It follows that analytical models must take into account the local contribution to the far-field noise induced by the streamwise variation of the hydrodynamic pressure on the serration surface.

Effect of drop size on the impact thermodynamics for supercooled large droplet in aircraft icing

Abstract: Supercooled large droplet (SLD), which can cause abnormal icing, is a well-known issue in aerospace engineering. Although efforts have been exerted to understand large droplet impact dynamics and the supercooled feature in the film/substrate interface, respectively, the thermodynamic effect during the SLD impact process has not received sufficient attention. This work conducts experimental studies to determine the effects of drop size on the thermodynamics for supercooled large droplet impingement. Through phenomenological reproduction, the rapid-freezing characteristics are observed in diameters of 400, 800, and 1300 μm. The experimental analysis provides information on the maximum spreading rate and the shrinkage rate of the drop, the supercooled diffusive rate, and the freezing time. A physical explanation of this unsteady heat transfer process is proposed theoretically, which indicates that the drop size is a critical factor influencing the supercooled heat exchange and effective heat transfer duration between the film/substrate interface. On the basis of the present experimental data and theoretical analysis, an impinging heating model is developed and applied to typical SLD cases. The model behaves as anticipated, which underlines the wide applicability to SLD icing problems in related fields.

Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality

Abstract: Flexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust.

Marangoni flow at droplet interfaces: Three-dimensional solution and applications

Abstract: The Marangoni effect refers to fluid flow induced by a gradient in surface tension at a fluid-fluid interface. We determine the full three-dimensional Marangoni flow generated by a non-uniform surface tension profile at the interface of a self-propelled spherical emulsion droplet. For all flow fields inside, outside, and at the interface of the droplet, we give analytical formulas. We also calculate the droplet velocity vector vD, which describes the swimming kinematics of the droplet, and generalize the squirmer parameter β, which distinguishes between different swimmer types called neutral, pusher, or puller. In the second part of this paper, we present two illustrative examples, where the Marangoni effect is used in active emulsion droplets. First, we demonstrate how micelle adsorption can spontaneously break the isotropic symmetry of an initially surfactant-free emulsion droplet, which then performs directed motion. Second, we think about light-switchable surfactants and laser light to create a patch with a different surfactant type at the droplet interface. Depending on the setup such as the wavelength of the laser light and the surfactant type in the outer bulk fluid, one can either push droplets along unstable trajectories or pull them along straight or oscillatory trajectories regulated by specific parameters. We explore these cases for strongly absorbing and for transparent droplets.

Vorticity transformation in high Karlovitz number premixed flames

Abstract: To better understand the two-way coupling between turbulence and chemistry, the changes in turbulence characteristics through a premixed flame are investigated. Specifically, this study focuses on vorticity, ω, which is characteristic of the smallest length and time scales of turbulence, analyzing its behavior within and across high Karlovitz number (Ka) premixed flames. This is accomplished through a series of direct numerical simulations (DNS) of premixed n-heptane/air flames, modeled with a 35-species finite-rate chemical mechanism, whose conditions span a wide range of unburnt Karlovitz numbers and flame density ratios. The behavior of the terms in the enstrophy, ω^2 = ω ⋅ ω, transport equation is analyzed, and a scaling is proposed for each term. The resulting normalized enstrophy transport equation involves only a small set of parameters. Specifically, the theoretical analysis and DNS results support that, at high Karlovitz number, enstrophy transport obtains a balance of the viscous dissipation and production/vortex stretching terms. It is shown that, as a result, vorticity scales in the same manner as in homogeneous, isotropic turbulence within and across the flame, namely, scaling with the inverse of the Kolmogorov time scale, τ_η. As τ_η is a function only of the viscosity and dissipation rate, this work supports the validity of Kolmogorov’s first similarity hypothesis in premixed turbulentflames for sufficiently high Ka numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and finally the physical configuration.

Experimental study of transonic buffet phenomenon on a 3D swept wing

Abstract: The objective of this paper is to analyze the 3D buffet phenomenon which appears on a swept wing at a high Mach number and/or high angle of attack. This aerodynamic instability induces strong wall pressure fluctuations and as such limits aircraft envelope. Consequently, it is interesting to understand this phenomenon in order to not only improve aircraft performance but also to provide more flexibility during the design phase. Results from two wind tunnel tests on a 3D half wing-body configuration are presented for several freestream Mach numbers (0.78–0.86) and Reynolds numbers (2.83 × 106–8.49 × 106, based on the aerodynamic mean chord). The buffet phenomenon is characterized using steady and unsteady wall pressure measurements. By opposition to the 2D buffet which exhibits rather a well marked peak in the pressure spectra, the 3D buffet is characterized by a broadband bump at a much higher Strouhal number (between 4 and 7 times higher). It is also observed that two different instabilities coexist on th...

Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows

Abstract: Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are “minimal” in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx ≳ 2Lz, Ly ≳ Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx ≳ 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ∼20S−1, and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general.

On determining characteristic length scales in pressure-gradient turbulent boundary layers

Abstract: In the present work we analyze three commonly used methods to determine the edge of pressure gradient turbulent boundary layers: two based on composite profiles, the one by Chauhan et al. (Fluid Dy ...

Plane shock wave interaction with a cylindrical water column

Abstract: A complex system of waves propagating inside a water column due to the impact of plane shock wave is investigated both experimentally and numerically. Flow features, such as, focusing of expansion ...

Investigation on subsonic to supersonic flow around a sphere at low Reynolds number of between 50 and 300 by direct numerical simulation

Abstract: In this study, analysis of flow properties around a sphere and its aerodynamic coefficients in the high-Mach-and-low-Reynolds-numbers conditions is carried out by direct numerical simulations solving the three-dimensional compressible Navier–Stokes equations. The calculation is performed on a boundary-fitted coordinate system with a high-order scheme of sufficient accuracy. The analysis is conducted by assuming a rigid sphere with a Reynolds number of between 50 and 300, based on the diameter of the sphere and the freestream velocity and a freestream Mach number of between 0.3 and 2.0, together with the adiabatic wall boundary condition. The calculation shows the following yields: (1) unsteady fluctuation of hydrodynamic forces become smaller as the Mach number increases under the same Reynolds number condition, (2) the drag coefficient increases with the Mach number due to an increase in the pressure drag by the shock wave, and (3) an accurate prediction of the drag coefficient in the supersonic regime using traditional models might be difficult.

Similarity transformation approach for ferromagnetic mixed convection flow in the presence of chemically reactive magnetic dipole

Abstract: A simple model of chemical reactions for two dimensional ferrofluid flows is constructed. The impact of magnetic dipole and mixed convection is further analyzed. Flow is caused by linear stretching of the sheet. Similarity transformation is adopted to convert the partial differential equations into ordinary differential equations and then solved by Euler’s explicit method. The characteristics of sundry parameters on the velocity, temperature, and concentration fields are graphically elaborated. It is noted that the impact of magneto-thermomechanical interaction is to slow down the fluid motion. The skin friction coefficient enhances and affects the rate of heat transfer. For higher values of ferrohydrodynamics, the interaction velocity shows decreasing behavior. Further the Prandtl number on temperature has opposite behavior when compared with thermal radiation and ferrohydrodynamics interaction.

Multi-dimensional rheology-based two-phase model for sediment transport and applications to sheet flow and pipeline scour

Abstract: Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial, and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − e turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.

High fidelity simulation and analysis of liquid jet atomization in a gaseous crossflow at intermediate Weber numbers

Abstract: Recent advances in numerical methods coupled with the substantial enhancements in computing power and the advent of high performance computing have presented first principle, high fidelity simulation as a viable tool in the prediction and analysis of spray atomization processes. The credibility and potential impact of such simulations, however, has been hampered by the relative absence of detailed validation against experimental evidence. The numerical stability and accuracy challenges arising from the need to simulate the high liquid-gas density ratio across the sharp interfaces encountered in these flows are key reasons for this. In this work we challenge this status quo by presenting a numerical model able to deal with these challenges, employing it in simulations of liquid jet in crossflow atomization and performing extensive validation of its results against a carefully executed experiment with detailed measurements in the atomization region. We then proceed to the detailed analysis of the flow physics. The computational model employs the coupled level set and volume of fluid approach to directly capture the spatiotemporal evolution of the liquid-gas interface and the sharp-interface ghost fluid method to stably handle high liquid-air density ratio. Adaptive mesh refinement and Lagrangian droplet models are shown to be viable options for computational cost reduction. Moreover, high performance computing is leveraged to manage the computational cost. The experiment selected for validation eliminates the impact of inlet liquid and gas turbulence and focuses on the impact of the crossflow aerodynamic forces on the atomization physics. Validation is demonstrated by comparing column surface wavelengths, deformation, breakup locations, column trajectories and droplet sizes, velocities, and mass rates for a range of intermediate Weber numbers. Analysis of the physics is performed in terms of the instability and breakup characteristics and the features of downstream flow recirculation, and vortex shedding. Formation of “Λ” shape windward column waves is observed and explained by the combined upward and lateral surface motion. The existence of Rayleigh-Taylor instability as the primary mechanism for the windward column waves is verified for this case by comparing wavelengths from the simulations to those predicted by linear stability analyses. Physical arguments are employed to postulate that the type of instability manifested may be related to conditions such as the gas Weber number and the inlet turbulence level. The decreased column wavelength with increasing Weber number is found to cause enhanced surface stripping and early depletion of liquid core at higher Weber number. A peculiar “three-streak-two-membrane” liquid structure is identified at the lowest Weber number and explained as the consequence of the symmetric recirculation zones behind the jet column. It is found that the vortical flow downstream of the liquid column resembles a von Karman vortex street and that the coupling between the gas flow and droplet transport is weak for the conditions explored.

Experimental study on the interaction between bubble and free surface using a high-voltage spark generator

Abstract: The experimental studies presented in this paper attempt to supply a reasonable comprehensive explanation for the key feature of the collapse bubble and the complex nature of the raised free surface. Six distinctive patterns of free surface motion were identified for bubbles initiated at different γf (the non-dimensional bubble-free surface distance scaled with the maximum bubble radius). Special features such as “breaking wrinkles,” “spraying water film,” and other unstable phenomena were observed with free surface motions, which were hardly captured by a boundary integral scheme. Parameters defining the shape of the free surface, such as the spike height Hspike, the spike width Wbase, and the skirt height Hspray, are measured and analyzed against γf. Different voltages were used to generate bubbles with varies sizes, while the bubble and free surface motion patterns appeared to be largely independent of the bubble size. Finally, collapsing bubble shape, centroid migration, period of bubble oscillation, ...

On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces

Abstract: Superhydrophobic surfaces can significantly reduce hydrodynamic skin drag by accommodating large slip velocity near the surface due to entrapment of air bubbles within their micro-scale roughness elements. While there are many Stokes flow solutions for flows near superhydrophobic surfaces that describe the relation between effective slip length and surface geometry, such relations are not fully known in the turbulent flow limit. In this work, we present a phenomenological model for the kinematics of flow near a superhydrophobic surface with periodic post-patterns at high Reynolds numbers. The model predicts an inverse square root scaling with solid fraction, and a cube root scaling of the slip length with pattern size, which is different from the reported scaling in the Stokes flow limit. A mixed model is then proposed that recovers both Stokes flow solution and the presented scaling, respectively, in the small and large texture size limits. This model is validated using direct numerical simulations of turbulent flows over superhydrophobic posts over a wide range of texture sizes from L+ ≈ 6 to 310 and solid fractions from ϕs = 1/9 to 1/64. Our report also embarks on the extension of friction laws of turbulent wall-bounded flows to superhydrophobic surfaces. To this end, we present a review of a simplified model for the mean velocity profile, which we call the shifted-turbulent boundary layer model, and address two previous shortcomings regarding the closure and accuracy of this model. Furthermore, we address the process of homogenization of the texture effect to an effective slip length by investigating correlations between slip velocity and shear over pattern-averaged data for streamwise and spanwise directions. For L+ of up to O(10), shear stress and slip velocity are perfectly correlated and well described by a homogenized slip length consistent with Stokes flow solutions. In contrast, in the limit of large L+, the pattern-averaged shear stress and slip velocity become uncorrelated and thus the homogenized boundary condition is unable to capture the bulk behavior of the patterned surface.

Investigation of drop impact on dry and wet surfaces with consideration of surrounding air

Abstract: Numerical simulations were conducted to investigate drop impingement and splashing on both dry and wet surfaces at impact velocities greater than 50 m/s with the consideration of the effect of surrounding air. The Navier-Stokes equations were solved using the variable density pressure projection method on a dynamic block structured adaptive grid. The moment of fluid method was used to reconstruct interfaces separating different phases. A dynamic contact angle model was used to define the boundary condition at the moving contact line. Simulations showed that lowering the ambient gas density can suppress dry surface splashing, which is in agreement with the experiments. A recirculation zone was observed inside the drop after contact: a larger recirculation zone was formed earlier in the higher gas density case than in the lower gas density case. Increasing gas density also enhances the creation of secondary droplets from the lamella breakup. For high speed impact on a dry surface, lowering ambient gas density attenuates splashing. However, ambient air does not significantly affect splashing on a wet surface. Simulations showed that the splashed droplets are primarily from the exiting liquid film.

Numerical simulation of a collapsing bubble subject to gravity

Abstract: The present paper focuses on the simulation of the expansion and aspherical collapse of a laser-generated bubble subjected to an acceleration field and comparison of the results with instances from high-speed videos. The interaction of the liquid and gas is handled with the volume of fluid method. Compressibility effects have been included for each phase to predict the propagation of pressure waves. Initial conditions were estimated through the Rayleigh Plesset equation, based on the maximum bubble size and collapse time. The simulation predictions indicate that during the expansion the bubble shape is very close to spherical. On the other hand, during the collapse the bubble point closest to the bottom of the container develops a slightly higher collapse velocity than the rest of the bubble surface. Over time, this causes momentum focusing and leads to a positive feedback mechanism that amplifies the collapse locally. At the latest collapse stages, a jet is formed at the axis of symmetry, with opposite direction to the acceleration vector, reaching velocities of even 300 m/s. The simulation results agree with the observed bubble evolution and pattern from the experiments, obtained using high speed imaging, showing the collapse mechanism in great detail and clarity.

The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions

Abstract: We study the effect of varying the mass and volume fraction of a suspension of rigid spheres dispersed in a turbulent channel flow. We performed several direct numerical simulations using an immersed boundary method for finite-size particles changing the solid to fluid density ratio R, the mass fraction χ, and the volume fraction ϕ. We find that varying the density ratio R between 1 and 10 at constant volume fraction does not alter the flow statistics as much as when varying the volume fraction ϕ at constant R and at constant mass fraction. Interestingly, the increase in overall drag found when varying the volume fraction is considerably higher than that obtained for increasing density ratios at same volume fraction. The main effect at density ratios R of the order of 10 is a strong shear-induced migration towards the centerline of the channel. When the density ratio R is further increased up to 1000, the particle dynamics decouple from that of the fluid. The solid phase behaves as a dense gas and the fluid and solid phase statistics drastically change. In this regime, the collision rate is high and dominated by the normal relative velocity among particles.