Fluids — Open Access Journal

The majority of aerospace structural composites use thermoset resins for their processing flexibility, temperature capability, and environmental durability. In this study, the recovery behavior of Veriflex-E, an epoxy-based, thermosetting, thermally-triggered shape memory polymer (SMP) resin, is investigated in glassy (25 °C) and rubbery (130 °C) states, as a function of shape memory cycles, and as a means to evaluate its potential as a resin for a shape memory composite. At 25 °C, Veriflex-E exhibits a promising high elastic modulus and a positive, nonlinear strain rate sensitivity in monotonic loading. At 130 °C, the strain rate sensitivity in monotonic loading decreases. Stress relaxation after storage in the deformed temporary state and subsequent shape recovery is of particular interest, a challenge to measure, and has not been widely reported for SMPs. The current experimental program measures the influence of strain rate changes in the 10⁻⁴–10⁻² s⁻¹ range on the stress relaxation response of the material, as well as on the strain recovery behavior at both 25 °C and 130 °C. As expected, the post-relaxation strain is larger with faster loading. Unexpectedly, the total strain recovered after shape memory cycling is more similar to the low temperature deformation. Overall, the results suggest that, while being influenced by both the loading rate and the test temperature, Veriflex-E is a promising candidate for a shape memory composite which could enable adaptive structures. Full article

This paper presents an autobiographical and biographical historical account of the genesis, evolution and resolution of the Elder Problem. It begins with John W. Elder and his autobiographical story leading to his groundbreaking work on natural convection at Cambridge in the 1960’s. His seminal work published in the Journal of Fluid Mechanics in 1967 became the basis for the modern benchmark of variable density flow simulators that we know today as “The Elder Problem”. There have been well known and major challenges with the Elder Problem model benchmark—notably the multiple solutions that were ultimately uncovered using different numerical models. Most recently, it has been shown that the multiple solutions are indeed physically realistic bifurcation solutions to the Elder Problem and not numerically spurious artefacts. The quandary of the Elder Problem has now been solved—a major scientific breakthrough for fluid mechanics and for numerical modelling. This paper—records, reflections, reminiscences, stories and anecdotes—is an historical autobiographical and biographical memoir. It is the personal story of the Elder Problem told by some of the key scientists who established and solved the Elder Problem. 2017 marks the 50 year anniversary of the classical work by John W. Elder published in Journal of Fluid Mechanics in 1967. This set the stage for this scientific story over some five decades. This paper is a celebration and commemoration of the life and times of John W. Elder, the problem named in his honour, and some of the key scientists who worked on, and ultimately solved, it. Full article

Non-equilibrium molecular dynamics simulations are widely employed to study transport fluid properties. Observables measured at the atomistic level can serve as inputs for continuum calculations, allowing for improved analysis of phenomena involving multiple scales. In hybrid modelling, uncertainties present in the information transferred across scales can have a significant impact on the final predictions. This work shows the influence of force-field variability on molecular measurements of the shear viscosity of water. In addition, the uncertainty propagation is demonstrated by quantifying the sensitivity of continuum velocity distribution to the particle-based calculations. The uncertainty is modelled with polynomial chaos expansion using a non-intrusive spectral projection strategy. The analysis confirms that low-order polynomial basis are sufficient to calculate the dispersion of observables. Full article

Blood viscosity is a crucial element for any computation of flow fields in the vasculature or blood-wetted devices. Although blood is comprised of multiple elements, and its viscosity can vary widely depending on several factors, in practical applications, it is commonly assumed to be a homogeneous, Newtonian fluid with a nominal viscosity typically of 3.5 cP. Two quasi-mechanistic models for viscosity are presented here, built on the foundation of the Krieger model of suspensions, in which dependencies on shear rate, hematocrit, and plasma protein concentrations are explicitly represented. A 3-parameter Asymptotic Krieger model (AKM) exhibited excellent agreement with published Couette experiments over four decades of shear rate (0–1000 s-1, root mean square (RMS) error = 0.21 cP). A 5-parameter Modified Krieger Model (MKM5) also demonstrated a very good fit to the data (RMS error = 1.74 cP). These models avoid discontinuities exhibited by previous models with respect to hematocrit and shear rate. In summary, the quasi-mechanistic, Modified-Krieger Model presented here offers a reasonable compromise in complexity to provide flexibility to account for several factors that affect viscosity in practical applications, while assuring accuracy and stability. Full article

Working fluids possess several applications in manufacturing processes, for instance lubricants in metals machining. Typical metal working fluids are formulated as oil-in-water emulsions. The maintenance of the physical stability of the working fluid during operation is a key factor for the sustainability of the relevant process. Therefore, continuous control of the working fluids stability and performance during machine operation is an essential tool for maintenance of the process performance. Turbidity measurement (TM) is a process technique for emulsion stability and quality assessment, where light transmission and absorption of an emulsion system is analyzed. However, for in-process measurement and fluid quality detection during the machine operation by TM, it is necessary to implement a transmission inline sensor into the working fluid flow line. The continuous flow measurement may cause problems for long-term sensor operation regarding, e.g., biofouling of the sensor optical glasses or erroneous measurements due to emulsion droplets segregation effects. In the present investigation, computational fluid dynamic (CFD) simulations have been adapted to obtain the emulsion flow conditions within a typical TM sensor probe, thereby allowing an assessment of the adhesion probability of microorganisms as well as droplet segregation effects. The simulation results indicate some temporal changes of the dispersed phase concentration in the detected emulsion flow. Due to droplet segregation in the emulsion, the flow velocity needs to exceed a certain value for reliable operation. It is shown here that in this flow regime microbiological attachments on the probe surfaces may be sufficiently avoided. A minimum critical flow velocity is derived to avoid biomolecule adhesion and thus durable operation of the sensor. Full article

Since the pioneering work of Taylor, the analysis of flow regimes of incompressible, viscous fluids contained in circular Couette systems with independently rotating cylinders have charmed many researchers. The characteristics of such kind of flows have been considered for some industrial applications. Recently, Taylor-Couette flows found an innovative application in the production of optical fiber nanotips, to be used in molecular biology and medical diagnostic fields. Starting from the activity of Barucci et al., the present work concerns the numerical analysis of a Taylor-Couette system composed by two coaxial counter-rotating cylinders with low aspect ratio and radius ratio, filled with three stratified fluids. An accurate analysis of the flow regimes is performed, considering both the variation of inner and outer rotational speed and the reduction of fiber radius due to etching process. The large variety of individuated flow configurations provides useful information about the possible use of the Taylor-Couette system in a wide range of engineering applications. For the present case, the final objective is to provide accurate information to manufacturers of fiber nanotips about the expected flow regimes, thus helping them in the setup of the control process that will be used to generate high-quality products. Full article

Oceanic and atmospheric dynamics are often interpreted through potential vorticity, as this quantity is conserved along the geostrophic flow. However, in addition to potential vorticity, surface buoyancy is a conserved quantity, and this also affects the dynamics. Buoyancy at the ocean surface or at the atmospheric tropopause plays the same role of an active tracer as potential vorticity does since the velocity field can be deduced from these quantities. The surface quasi-geostrophic model has been proposed to explain the dynamics associated with surface buoyancy conservation and seems appealing for both the ocean and the atmosphere. In this review, we present its main characteristics in terms of coherent structures, instabilities and turbulent cascades. Furthermore, this model is mathematically studied for the possible formation of singularities, as it presents some analogies with three-dimensional Euler equations. Finally, we discuss its relevance for the ocean and the atmosphere. Full article

A simple model of nonlinear salt-finger convection in two dimensions is derived and studied. The model is valid in the limit of a small solute to heat diffusivity ratio and a large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modified Rayleigh–Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute field and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identified for the second model: the weakly driven regime is characterized by a large-scale flow associated with a balance between advection and linear instability, while the strongly-driven regime produces multiscale structures, resulting in a balance between energy input through linear instability and energy transfer between scales. For both regimes, we analytically predict and numerically confirm the dependence of the kinetic energy and salinity fluxes on the ratio between solutal and thermal Rayleigh numbers. The spectra and probability density functions are also computed. Full article

The flow of a non-Newtonian, power-law fluid, directed normally to long, two-dimensional horizontal bodies, is considered in the present note. It is found that for low Reynolds numbers ($\mathrm{Re}\le 0.1$) and a low power-law index (shear-thinning fluids) the drag coefficient always obeys the relationship $c_D=A/\mathrm{Re}$, whereas at a high power-law index (shear-thickening fluids) the drag coefficient tends to become identical for all bodies irrespective of their cross-section form. Full article

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior of these forces as a function of the flow speed and fiber orientation. The Vogel exponents, which characterize the rate of bending of a fiber in a flow, are found for the various configurations examined here and seem to display interesting variations. These exponents are then compared with our previously studied two-dimensional models. Full article

An analysis of 2D subsonic flow over an NACA 0015 airfoil with a 30% trailing edge flap at a constant Reynolds number of 10⁶ for various incidence angles and a range of flap deflections is presented. The steady-state governing equations of continuity and momentum conservation are solved combined with the realizable k-ε turbulence model using the ANSYS-Fluent code (Version 13.7, ANSYS, Inc., Canonsburg, PA, USA). The primary objective of the study is to provide a comprehensive understanding of flow characteristics around the NACA 0015 airfoil as a function of the angle of attack and flap deflection at Re = 10⁶ using the realizable k-ε turbulence model. The results are validated through comparison of the predictions with the free field experimental measurements. Consistent with the experimental observations, the numerical results show that increased flap deflections increase the maximum lift coefficient, move the zero-lift angle of attack (AoA) to a more negative value, decrease the stall AoA, while the slope of the lift curve remains unchanged and the curve just shifts upwards. In addition, the numerical simulations provide limits for lift increment $\Delta C_l$ and C_{l, max} values to be 1.1 and 2.2, respectively, obtained at a flap deflection of 50°. This investigation demonstrates that the realizable k-ε turbulence model is capable of predicting flow features over an airfoil with and without flap deflections with reasonable accuracy. Full article

Pulsatile flow in a 3D model of arterial double stenoses is investigated using a large eddy simulation (LES) technique. The computational domain that has been chosen is a simple channel with a biological-type stenosis formed eccentrically on the top wall. The pulsation was generated at the inlet using the first four harmonics of the Fourier series of the pressure pulse. The flow Reynolds numbers, which are typically suitable for a large human artery, are chosen in the present work. In LES, a top-hat spatial grid-filter is applied to the Navier–Stokes equations of motion to separate the large-scale flows from the sub-grid scale (SGS). The large-scale flows are then resolved fully while the unresolved SGS motions are modelled using a localized dynamic model. It is found that the narrowing of the channel causes the pulsatile flow to undergo a transition to a turbulent condition in the downstream region; as a consequence, a severe level of turbulent fluctuations is achieved in these zones. Transitions to turbulent of the pulsatile flow in the post stenosis are examined through the various numerical results, such as velocity, streamlines, wall pressure, shear stresses and root mean square turbulent fluctuations. Full article

Use of laminar flow-derived power law models to predict hemolysis with turbulence remains problematical. Flows in a Couette viscometer and a capillary tube have been simulated to investigate various combinations of Reynolds and/or viscous stresses power law models for hemolysis prediction. A finite volume-based computational method provided Reynolds and viscous stresses so that the effects of area-averaged and time-averaged Reynolds stresses, as well as total, viscous, and wall shear on hemolysis prediction could be assessed. The flow computations were conducted by using Reynolds-Averaged Navier-Stokes models of turbulence (k-ε and k-ω SST) to simulate four different experimental conditions in a capillary tube and seven experimental conditions in a Couette viscometer taken from the literature. Power law models were compared by calculating standard errors between measured hemolysis values and those derived from power law models with data from the simulations. In addition, suitability of Reynolds and viscous stresses was studied by threshold analysis. Results showed there was no evidence of a threshold value for hemolysis in terms of Reynolds and viscous stresses. Therefore, Reynolds and viscous stresses are not good predictors of hemolysis. Of power law models, the Zhang power law model (Artificial Organs, 2011, 35, 1180–1186) gives the lowest error overall for the hemolysis index and Reynolds stress (0.05570), while Giersiepen’s model (The International journal of Artificial Organs, 1990, 13, 300–306) yields the highest (6.6658), and intermediate errors are found through use of Heuser’s (Biorheology, 1980, 17, 17–24) model (0.3861) and Fraser’s (Journal of Biomechanical Engineering, 2012, 134, 081002) model (0.3947). Full article

In this study, the linear stability of an unsteady thermal boundary layer in a semi-infinite porous medium is considered. This boundary layer is induced by varying the temperature of the horizontal boundary sinusoidally in time about the ambient temperature of the porous medium; this mimics diurnal heating and cooling from above in subsurface groundwater. Thus if instability occurs, this will happen in those regions where cold fluid lies above hot fluid, and this is not necessarily a region that includes the bounding surface. A linear stability analysis is performed using small-amplitude disturbances of the form of monochromatic cells with wavenumber, k. This yields a parabolic system describing the time-evolution of small-amplitude disturbances which are solved using the Keller box method. The critical Darcy-Rayleigh number as a function of the wavenumber is found by iterating on the Darcy-Rayleigh number so that no mean growth occurs over one forcing period. It is found that the most dangerous disturbance has a period which is twice that of the underlying basic state. Cells that rotate clockwise at first tend to rise upwards from the surface and weaken, but they induce an anticlockwise cell near the surface at the end of one forcing period, which is otherwise identical to the clockwise cell found at the start of that forcing period. Full article

A comprehensive review of the fundamental rheology of dilute disperse systems is presented. The exact rheological constitutive equations based on rigorous single-particle mechanics are discussed for a variety of disperse systems. The different types of inclusions (disperse phase) considered are: rigid-solid spherical particles with and without electric charge, rigid-porous spherical particles, non-rigid (soft) solid particles, liquid droplets with and without surfactant, bubbles with and without surfactant, capsules, core-shell particles, non-spherical solid particles, and ferromagnetic spherical and non-spherical particles. In general, the state of the art is good in terms of the theoretical development. However, more experimental work is needed to verify the theoretical models and to determine their range of validity. This is especially true for dispersions of porous particles, capsules, core-shell particles, and magnetic particles. The main limitation of the existing theoretical developments on the rheology of disperse systems is that the matrix fluid is generally assumed to be Newtonian in nature. Rigorous theoretical models for the rheology of disperse systems consisting of non-Newtonian fluid as the matrix phase are generally lacking, especially at arbitrary flow strengths. Full article

Traditionally, the formation of the Counter-Rotating Vortex Pair (CRVP) has been attributed to three main sources: the jet-mainstream shear layer where the jet meets with the mainstream flow right outside the pipe, the in-tube boundary layer developing along the pipe wall, and the in-tube vortices associated with the tube inlet vorticity; whereas the liftoff-reattachment phenomenon occurring in the main flow along the plate right downstream of the jet has been associated with the jet flow trajectory. The jet-mainstream shear layer has also been demonstrated to be the dominant source of CRVP formation, whereby the shear layer disintegrates into vortex rings that deform as the jet convects downstream, becoming a pair of CRVPs flowing within the jet and eventually turning into the main flow direction. These traditional findings are assessed qualitatively and quantitatively for film-cooling flow in gas turbines by simulating numerically the flow and evaluating the extent to which the traditional flow phenomena are taking place particularly for CRVP and for flow liftoff-reattachment. To this end, three flow simulation cases are used; they are referred to as 1—the baseline case; 2—the free-slip in-tube wall case (FSIT); and 3—the unsteady flow case. The baseline case is a typical film-cooling case. The FSIT case is used to assess the in-tube boundary layer. Cases 1 and 2 are simulated using the Reynolds-averaged Navier-Stokes equations (RANS), whereas Case 3 solves a Detached Eddy Simulation (DES) model. It is concluded that decreasing the strength of the CRVP, which is the case for e.g., shaped holes, provides high cooling performance, and the liftoff-reattachment phenomenon was thus found to be strongly influenced by the entrainment caused by the CRVP, rather than the jet flow trajectory. These interpretations of the flow physics that are more relevant to gas turbine cooling flow are new and provide a physics-based guideline for designing new film-cooling schemes. Full article

A thrombus is a blood clot that forms on a surface, and can grow and detach, presenting a high risk for stroke and pulmonary embolism. This risk increases with blood-contacting medical devices, due to the immunological response to foreign surfaces and altered flow patterns that activate the blood and promote thromboembolism (TE). Abnormal blood transport, including vortex behavior and regional stasis, can be assessed from Lagrangian Coherent Structures (LCS). LCS are flow structures that bound transport within a flow field and divide the flow into regions with maximally attracting/repelling surfaces that maximize local shear. LCS can be identified from finite time Lyapunov exponent (FTLE) fields, which are computed from velocity field data. In this study, the goal was to use FTLE analysis to evaluate LCS in the left ventricle (LV) using velocity data obtained from flow visualization of a mock circulatory loop. A model of dilated cardiomyopathy (DCM) was used to investigate the effect of left ventricular assist device (LVAD) support on diastolic filling and transport in the LV. A small thrombus in the left ventricular outflow tract was also considered using data from a corresponding LV model. The DCM LV exhibited a direct flow of 0.8 L/cardiac cycle, which was tripled during LVAD support Delayed ejection flow was doubled, further illustrating the impact of LVAD support on blood transport. An examination of the attracting LCS ridges during diastolic filling showed that the increase is due primarily to augmentation of A wave inflow, which is associated with increased vortex circulation, kinetic energy and Forward FTLE. The introduction of a small thrombus in the left ventricular outflow tract (LVOT) of the LV had a minimal effect on diastolic inflow, but obstructed systolic outflow leading to decreased transport compared with the unobstructed LVOT geometry. Localized FTLE in the LVOT increased dramatically with the small thrombus model, which reflects greater recirculation distal to the thrombus location. The combination of the thrombus and the LVAD increased stasis distal to the thrombus, increasing the likelihood of recurring coagulation during Series flow conditions. The extension of the results of the previous studies with this analysis provides a more sensitive indicator of TE risk than the Eulerian velocity values do, and may provide an important tool for evaluating medical device design, surgical implantation, and treatment options. Full article

The flow of a non-Newtonian, power-law fluid, directed normally to a horizontal cylinder with square cross-section (two-dimensional flow) is considered in the present paper. The problem is investigated numerically with a very large calculation domain in order that the flow could be considered unconfined. The investigation covers the power-law index from 0.1 up to 2 and the Reynolds number ranges from 60 to 160. Over this range of Reynolds numbers the flow is unsteady. It is found that the drag coefficient and the Strouhal number are higher in a confined flow compared to those of an unconfined flow. In addition some flow characteristics are lost in a confined flow. Complete results for the drag coefficient and Strouhal number in the entire shear-thinning and shear-thickening region have been produced. In shear-thinning fluids chaotic structures exist which diminish at higher values of power-law index. This study represents the first investigation of unsteady, non-Newtonian power-law flow past a square cylinder in an unconfined field. Full article

To investigate the translation of a compound particle in a highly viscous, incompressible fluid, we carry out an analytic study on flow past a fixed spherical compound particle. The spherical object is considered to have a rigid kernel covered with a fluid coating. The fluid within the coating has a different viscosity from that of the surrounding fluid and is immiscible with the surrounding fluid. The inertia effect is negligible for flows both inside the coating and outside the object. Thus, flows are in the Stokes regime. Taking advantage of the symmetry properties, we reduce the problem in two dimensions and derive the explicit formulae of the stream function in the polar coordinates. The no-slip boundary condition for the rigid kernel and the no interfacial mass transfer and force equilibrium conditions at fluid interfaces are considered. Two extreme cases: the uniform flow past a sphere and the uniform flow past a fluid drop, are reviewed. Then, for the fluid coating the spherical object, we derive the stream functions and investigate the flow field by the contour plots of stream functions. Contours of stream functions show circulation within the fluid coating. Additionally, we compare the drag and the terminal velocity of the object with a rigid sphere or a fluid droplet. Moreover, the extended results regarding the analytical solution for a compound particle with a rigid kernel and multiple layers of fluid coating are reported. Full article