Search

Immersed boundary methods (IBMs) are versatile and efficient computational techniques to solve flow problems in complex geometric configurations that retain the simplicity and efficiency of Cartesian structured meshes. Although these methods became known in the 1970s and gained credibility only in the new millennium, they had already been conceived and implemented at the beginning of the 1960s, even if the early computers of those times did not allow researchers to exploit their potential. Nowadays IBMs are established numerical schemes employed for the solution of many complex problems in which fluid mechanics may account for only part of the multiphysics dynamics. Despite the indisputable advantages, these methods also have drawbacks, and each problem should be carefully analyzed before deciding which particular IBM implementation is most suitable and whether additional modeling is necessary. High–Reynolds number flows constitute one of the main limitations of IBMs owing to the resolution of thin wall shear layers, which cannot benefit from anisotropic grid refinement at the boundaries. To alleviate this weakness, researchers have developed IBM-compliant wall models and local grid refinement strategies, although in these cases possible pitfalls must also be considered.

The icy moons of the solar system show several phenomena in their polar regions like active geysers or a thinner crust than at the equator, all of which might be related to a non-uniform heat transport in the underlying ocean of liquid water. We investigate the potential for local heat transport enhancement in these sub-glacial oceans by conducting direct numerical simulations of rotating Rayleigh-Bénard convection (RRBC) in spherical geometry at a water-like Prandtl number Pr=4.38, Rayleigh number Ra=106, and Rossby number ∞≥Ro≥0.03 (or in terms of the Ekman number ∞≥Ek≥6.28·10-5). We probe two ratios of inner to outer radius η=ri/ro=0.6 and η=0.8, which is closer to the presumed conditions on most icy moons, for different gravitational laws g(r)∝rγ. The simulations cover the full range from zero to rapid rotation close to where convection ceases, and therefore cross the rotation-affected regime of intermediate rotation rates with a potentially enhanced dimensionless heat transport Nu>Nunon–rot as known from planar RRBC.Although the global heat transport does not increase (Nuglobal≤Nunon–rot), we find an enhancement up to 28% at high latitudes around the poles (Nuhl>Nunon–rot), which is compensated by a reduced heat transport at low latitudes around the equator (Null

Immiscible and incompressible liquid–liquid flows are considered in a Taylor–Couette geometry and analysed by direct numerical simulations coupled with the volume-of-fluid method and a continuum surface force model. The system Reynolds number $Re \equiv r_i \omega _i d / \nu$ is fixed to $960$ , where the single-phase flow is in the steady Taylor vortex regime, whereas the secondary-phase volume fraction $\varphi$ and the system Weber number $We \equiv \rho r_i^2 \omega _i^2 d / \sigma$ are varied to study the interactions between the interface and the Taylor vortices. We show that different Weber numbers lead to two distinctive flow regimes, namely an advection-dominated regime and an interface-dominated regime. When $We$ is high, the interface is easily deformed because of its low surface tension. The flow patterns are then similar to the single-phase flow, and the system is dominated mainly by advection (advection-dominated regime). However, when $We$ is low, the surface tension is so large that stable interfacial structures with sizes comparable to the cylinder gap can exist. The background velocity field is modulated largely by these persistent structures, thus the overall flow dynamics is governed by the interface (interface-dominated regime). The effect of the interface on the global system response is assessed by evaluating the Nusselt number $Nu_{\omega }$ based on the non-dimensional angular velocity transport. It shows non-monotonic trends as functions of the volume fraction $\varphi$ for both low and high $We$ . We explain how these dependencies are closely linked to the velocity and interfacial structures.

We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to $Ra=10^{11}$ ) and three-dimensional (achieving Rayleigh number up to $Ra=10^9$ ) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wang et al. (Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

Motivated by the ablation of vertical ice faces in salt water, we use three-dimensional direct numerical simulations to investigate the heat and salt fluxes in two-scalar vertical convection. For parameters relevant to ice-ocean interfaces in the convection-dominated regime, we observe that the salinity field drives the convection and that heat is essentially transported as a passive scalar. By varying the diffusivity ratio of heat and salt (i.e., the Lewis number $Le$), we identify how the different molecular diffusivities affect the scalar fluxes through the system. Away from the walls, we find that the heat transport is determined by a turbulent Prandtl number of $Pr_t\approx 1$ and that double-diffusive effects are practically negligible. However, the difference in molecular diffusivities plays an important role close to the boundaries. In the (unrealistic) case where salt diffused faster than heat, the ratio of salt-to-heat fluxes would scale as $Le^{1/3}$, consistent with classical nested scalar boundary layers. However, in the realistic case of faster heat diffusion (relative to salt), we observe a transition towards a $Le^{1/2}$ scaling of the ratio of the fluxes. This coincides with the thermal boundary layer width growing beyond the thickness of the viscous boundary layer. We find that this transition is not determined by a critical Lewis number, but rather by a critical Prandtl number $Pr\approx 10$, slightly below that for cold seawater where $Pr=14$. We compare our results to similar studies of sheared and double-diffusive flow under ice shelves, and discuss the implications for fluxes in large-scale ice-ocean models. By coupling our results to ice-ocean interface thermodynamics, we describe how the flux ratio impacts the interfacial salinity, and hence the strength of solutal convection and the ablation rate., 17 pages, 9 figures

We perform direct numerical simulations to study the effect of the gravity centre offset in spherical Rayleigh–Bénard convection. When the gravity centre is shifted towards the south, we find that the shift of the gravity centre has a pronounced influence on the flow structures. At low Rayleigh number $Ra$ , a steady-state large-scale meridional circulation induced by the baroclinic imbalance, created by the misalignment of the gravity potentials and isotherms, is formed. At high $Ra$ , an energetic jet is created on the northern side of the inner sphere that is directed towards the outer sphere. The large-scale circulation induces a strong co-latitudinal dependence in the local heat flux. Nevertheless, the global heat flux is not affected by the changes in the large-scale flow organization induced by the gravity centre offset.

Spontaneous coronary artery dissection (SCAD) may occur in middle age population without any cardiovascular risk factor. We retrospectively evaluated anatomic features of 11 patients with SCAD using a coronary arteries computed tomography (CCT), compared to age and sex balanced patients who underwent CCT.CCT was performed in 11 patients (7 females and 4 males) as follow-up in patients with SCAD (left anterior descending - LAD or circumflex artery - Cx) and compared, using the propensity score matching analysis, with 11 healthy patients. Several anatomic features were evaluated: Left main (LM) length, angle between descending coronary artery (LAD) and its first branch, angle between LAD and LM, distance from the annulus to RCA (a-RCA distance) and LM (a-LM distance) ostia and their ratio; ratio between LM length and length a-LM and tortuosity score of the vessel with SCAD. A fluid dynamic analysis has been performed to evaluate the effects on shear stress of vessels wall.LM length was significantly shorter in patients with SCAD versus healthy subjects (P=0.01) as well as LM length/a-LM (P=0.03) and the angle between LAD and the first adjacent branch was sharper (P0.01). Tortuosity score showed a statistically significant difference between groups (P0.001). Fluid dynamic analysis demonstrates that, in SCAD group, an angle90 degree is present at the first bifurcation and it can be a cause of increased strain on vessel wall in patients with high tortuosity of coronary artery.Tortuosity and angle between the LAD and the adjacent arterial branch combined may determine increased shear stress on the vessel wall that increases the risk of SCAD.

Moderate rotation and moderate horizontal confinement similarly enhance the heat transport in Rayleigh–Bénard convection (RBC). Here, we systematically investigate how these two types of flow stabilization together affect the heat transport. We conduct direct numerical simulations of confined-rotating RBC in a cylindrical set-up at Prandtl number $\textit {Pr}=4.38$ , and various Rayleigh numbers $2\times 10^{8}\leqslant {\textit {Ra}}\leqslant 7\times 10^{9}$ . Within the parameter space of rotation (given as inverse Rossby number $0\leqslant {\textit {Ro}}^{-1}\leqslant 40$ ) and confinement (given as height-to-diameter aspect ratio $2\leqslant \varGamma ^{-1}\leqslant 32$ ), we observe three heat transport maxima. At lower $ {\textit {Ra}}$ , the combination of rotation and confinement can achieve larger heat transport than either rotation or confinement individually, whereas at higher $ {\textit {Ra}}$ , confinement alone is most effective in enhancing the heat transport. Further, we identify two effects enhancing the heat transport: (i) the ratio of kinetic and thermal boundary layer thicknesses controlling the efficiency of Ekman pumping, and (ii) the formation of a stable domain-spanning flow for an efficient vertical transport of the heat through the bulk. Their interfering efficiencies generate the multiple heat transport maxima.

This article presents an overview of the dynamics of the human heart and the main goal is the discussion of its fluid mechanic features. We will see, however, that the flow in the heart can not be fully described without considering its electrophysiology and elastomechanics as well as the interaction with the systemic and pulmonary circulations with which it is strongly connected. Biologically, the human heart is similar to that of all warm-blooded mammals and it satisfies the same allometric laws. Since the Paleolithic Age, however, humans have improved their living conditions, have modified the environment to satisfy their needs and, more recently, have developed advanced medical knowledge which has allowed triple the number of heartbeats with respect to other mammals. In the last century, effective diagnostic tools, reliable surgical procedures and prosthetic devices have been developed and refined leading to substantial progress in cardiology and heart surgery with routine clinical practice which nowadays cures many disorders, once lethal. Pulse duplicators have been built to reproduce the pulsatile flow and ‘blood analogues’, have been realized. Heart phantoms, can attain deformations similar to the real heart although the active contraction and the tissue anisotropy still can not be replicated. Numerical models have also become a viable alternative for cardiovascular research: they do not suffer from limitations of material properties and device technologies, thus making possible the realization of truly digital twins. Unfortunately, a high-fidelity model for the whole heart consists of a system of coupled, nonlinear partial differential equations with a number of degrees of freedom of the order of a billion and computational costs become the bottleneck. An additional challenge comes from the inherent human variability and the uncertainty of the heart parameters whose statistical assessment requires a campaign of simulations rather than a single deterministic calculation; reduced and surrogate models can be employed to alleviate the huge computational burden and all possibilities are currently being pursued. In the era of big data and artificial intelligence, cardiovascular research is also advancing by exploiting the latest technologies: equation-based augmented reality, virtual surgery and computational prediction of disease progression are just a few examples among many that will become standard practice in the forthcoming years.

Cardiac modeling entails the epistemic uncertainty of the input parameters, such as bundles and chambers geometry, electrical conductivities and cell parameters, thus calling for an uncertainty quantification (UQ) analysis. Since the cardiac activation and the subsequent muscular contraction is provided by a complex electrophysiology system made of interconnected conductive media, we focus here on the fast conductivity structures of the atria (internodal pathways) with the aim of identifying which of the uncertain inputs mostly influence the propagation of the depolarization front. Firstly, the distributions of the input parameters are calibrated using data available from the literature taking into account gender differences. The output quantities of interest (QoIs) of medical relevance are defined and a set of metamodels (one for each QoI) is then trained according to a polynomial chaos expansion (PCE) in order to run a global sensitivity analysis with non-linear variance-based Sobol’ indices with confidence intervals evaluated through the bootstrap method. The most sensitive parameters on each QoI are then identified for both genders showing the same order of importance of the model inputs on the electrical activation. Lastly, the probability distributions of the QoIs are obtained through a forward sensitivity analysis using the same trained metamodels. It results that several input parameters—including the position of the internodal pathways and the electrical impulse applied at the sinoatrial node—have a little influence on the QoIs studied. Vice-versa the electrical activation of the atrial fast conduction system is sensitive on the bundles geometry and electrical conductivities that need to be carefully measured or calibrated in order for the electrophysiology model to be accurate and predictive. Graphic Abstract: [Figure not available: see fulltext.].

While the heat transfer and the flow dynamics in a cylindrical Rayleigh-Bénard (RB) cell are rather independent of the aspect ratio Γ (diameter/height) for large Γ, a small-Γ cell considerably stabilizes the flow and thus affects the heat transfer. Here, we first theoretically and numerically show that the critical Rayleigh number for the onset of convection at given Γ follows Ra_{c,Γ}∼Ra_{c,∞}(1+CΓ^{-2})^{2}, with C≲1.49 for Oberbeck-Boussinesq (OB) conditions. We then show that, in a broad aspect ratio range (1/32)≤Γ≤32, the rescaling Ra→Ra_{ℓ}≡Ra[Γ^{2}/(C+Γ^{2})]^{3/2} collapses various OB numerical and almost-OB experimental heat transport data Nu(Ra,Γ). Our findings predict the Γ dependence of the onset of the ultimate regime Ra_{u,Γ}∼[Γ^{2}/(C+Γ^{2})]^{-3/2} in the OB case. This prediction is consistent with almost-OB experimental results (which only exist for Γ=1, 1/2, and 1/3) for the transition in OB RB convection and explains why, in small-Γ cells, much larger Ra (namely, by a factor Γ^{-3}) must be achieved to observe the ultimate regime.

Human respiratory events, such as coughing and sneezing, play an important role in the host-to-host airborne transmission of diseases. Thus, there has been a substantial effort in understanding these processes: various analytical or numerical models have been developed to describe them, but their validity has not been fully assessed due to the difficulty of a direct comparison with real human exhalations. In this study, we report a unique comparison between datasets that have both detailed measurements of a real human cough using spirometer and particle tracking velocimetry, and direct numerical simulation at similar conditions. By examining the experimental data, we find that the injection velocity at the mouth is not uni-directional. Instead, the droplets are injected into various directions, with their trajectories forming a cone shape in space. Furthermore, we find that the period of droplet emissions is much shorter than that of the cough: experimental results indicate that the droplets with an initial diameter ≳ 10 μ m are emitted within the first 0.05 s, whereas the cough duration is closer to 1 s. These two features (the spread in the direction of injection velocity and the short duration of droplet emission) are incorporated into our direct numerical simulation, leading to an improved agreement with the experimental measurements. Thus, to have accurate representations of human expulsions in respiratory models, it is imperative to include parametrisation of these two features.

We report on the mobility and orientation of finite-size, neutrally buoyant prolate ellipsoids (of aspect ratio $\Lambda=4$) in Taylor-Couette flow, using interface resolved numerical simulations. The setup consists of a particle-laden flow in between a rotating inner and a stationary outer cylinder. We simulate two particle sizes $\ell/d=0.1$ and $\ell/d=0.2$, $\ell$ denoting the particle major axis and $d$ the gap-width between the cylinders. The volume fractions are $0.01\%$ and $0.07\%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes $(i)$ to $(iii)$ are observed in the Taylor vortex flow regime, while mode ($iv$) encompasses both the wavy vortex, and turbulent Taylor vortex flow regimes. Mode $(i)$ corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit{Ta}$ range, particles get trapped in the Taylor vortex cores (mode ($ii$)). Mode $(iii)$ is the transition when both modes $(i)$ and $(ii)$ are observed. For mode $(iv)$, particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. We find the particle clustering for mode ($ii$) to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell/d=0.2$ compared to $\ell/d=0.1$. Secondly, the $\textit{Ta}$ range for which clustering is observed depends on the particle size. For this mode $(ii)$ we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell/d=0.2$ around $\textit{Ta}=4.2\times10^5$. This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ($\textit{Ta}=6\times10^5$) and we explain why., Comment: 22 pages, 12 figures

Enhancing the efficiency of water electrolysis, which can be severely impacted by the nucleation and growth of bubbles, is key in the energy transition. In this combined experimental and numerical study, in-situ bubble evolution and dissolution processes are imaged and compared to numerical simulations employing the immersed boundary method. We find that it is crucial to include solutal driven natural convection in order to represent the experimentally observed bubble behaviour even though such effects have commonly been neglected in modelling efforts so far. We reveal how the convective patterns depend on current densities and bubble spacings, leading to distinctively different bubble growth and shrinkage dynamics. Bubbles are seen to promote the convective instability if their spacing is large ($\geq4$mm for the present conditions), whereas the onset of convection is delayed if the inter-bubble distance is smaller. Our approach and our results can help devise efficient mass transfer solutions for gas evolving electrodes., 30 pages, 13 figures

The reliability of cardiovascular computational models depends on the accurate solution of the hemodynamics, the realistic characterization of the hyperelastic and electric properties of the tissues along with the correct description of their interaction. The resulting fluid–structure–electrophysiology interaction (FSEI) thus requires an immense computational power, usually available in large supercomputing centers, and requires long time to obtain results even if multi–CPU processors are used (MPI acceleration). In recent years, graphics processing units (GPUs) have emerged as a convenient platform for high performance computing, as they allow for considerable reductions of the time–to–solution. This approach is particularly appealing if the tool has to support medical decisions that require solutions within reduced times and possibly obtained by local computational resources. Accordingly, our multi–physics solver [1] has been ported to GPU architectures using CUDA Fortran to tackle fast and accurate hemodynamics simulations of the human heart without resorting to large–scale supercomputers. This work describes the use of CUDA to accelerate the FSEI on heterogeneous clusters, where both the CPUs and GPUs are used in synergistically with minor modifications of the original source code. The resulting GPU accelerated code solves a single heartbeat within a few hours (from three to ten depending on the grid resolution) running on premises computing facility made of few GPU cards, which can be easily installed in a medical laboratory or in a hospital, thus opening towards a systematic computational fluid dynamics (CFD) aided diagnostic.

We investigate the counter-intuitive initial decrease and subsequent increase in the Nusselt number $Nu$ with increasing wall Reynolds number $Re_w$ in the sheared Rayleigh–Bénard (RB) system by studying the energy spectra of convective flux and turbulent kinetic energy for Rayleigh number $Ra = 10^{7}$ , Prandtl number $Pr=1.0$ and inverse Richardson numbers $0 \leq 1/Ri \leq 10$ . These energy spectra show two distinct high-energy regions corresponding to the large-scale superstructures in the bulk and small-scale structures in the boundary layer (BL) regions. A greater separation between these scales at the thermal BL height correlates to a higher $Nu$ and indicates that the BLs are more turbulent. The minimum $Nu$ , which occurs at $1/Ri=1.0$ , is accompanied by the smallest separation between the large- and small-scale structures at the thermal BL height. At $1/Ri=1.0$ , we also observe the lowest value of turbulent kinetic energy normalized with the square of friction velocity within the thermal BL. Additionally, we find that the domain size has a limited effect on the heat and momentum transfer in the sheared RB system as long as the domain can accommodate the small-scale convective structures at the thermal BL height, signifying that capturing the large-scale superstructures is not essential to obtain converged values of $Nu$ and shear Reynolds number $Re_{\tau }$ . When the domain is smaller than these small-scale convective structures, the overall heat and momentum transfer reduces drastically.

We numerically investigate turbulent Rayleigh-B\'enard convection with gas bubbles attached to the hot plate, mimicking a core feature in electrolysis, catalysis, or boiling. The existence of bubbles on the plate reduces the global heat transfer due to the much lower thermal conductivity of gases as compared to liquids and changes the structure of the boundary layers. The numerical simulations are performed in 3D at Prandtl number Pr=4.38 (water) and Rayleigh number $10^7\le Ra \le10^8$. For simplicity, we assume the bubbles to be equally-sized and having pinned contact lines. We vary the total gas-covered area fraction $0.18 \le S_0 \le 0.62$, the relative bubble height $0.02\le h/H \le0.05$ (where $H$ is the height of the Rayleigh-B\'enard cell), the bubble number $40 \le n \le 144$, and their spatial distribution. In all cases, asymmetric temperature profiles are observed, which we quantitatively explain based on the heat flux conservation at each horizontal section. We further propose the idea of using an equivalent single-phase setup to mimic the system with attached bubbles. Based on this equivalence, we can calculate the heat transfer. Without introducing any free parameter, the predictions for the Nusselt number, the upper and lower thermal boundary layer thicknesses, and the mean centre temperature well agree with the numerical results. Finally, our predictions also work for the cases with much larger Pr (e.g. $400$), which indicates that our results can also be applied to predict the mass transfer in water electrolysis with bubbles attached to the electrode surface or in catalysis., Comment: 12 pages, 6 figures

How fast ice melts in turbulent flows is key to many natural and industrial processes, most notably the melting of ice in the polar regions. To get a better quantitative understanding of the physical mechanics at play, as a model system we pick vertical convection, consisting of ice and fresh water, and examine the lateral melting behavior through numerical simulations and theory. We find that the melting rate of ice as a function of an increasing heating temperature undergoes an abrupt transition from a slow- to a fast-melting state, contrary to the intuition of a gradual transition. The abrupt transition of the ice melting rate is due to the emergence of a reversed buoyant flow, due to the density anomaly of water near the melting point. A theoretical model based on energy conservation gives rise to a universal expression to relate the global heat fluxes and the ice melting rate which is consistent with our data. Besides their fundamental significance, our findings improve our understanding of how phase transitions couple to adjacent turbulent flow.

We study the statistics of passive scalars at $Pr=1$ , for turbulent flow within a smooth straight pipe of circular cross section up to $Re_{\tau } \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. While featuring a general organisation similar to the axial velocity field, passive scalar fields show additional energy at small wavenumbers, resulting in a higher degree of mixing and in a $k^{-4/3}$ spectral inertial range. The DNS results highlight logarithmic growth of the inner-scaled bulk and mean centreline scalar values with the friction Reynolds number, implying an estimated scalar von Kármán constant $k_{\theta } \approx 0.459$ , which also nicely fits the mean scalar profiles. The DNS data are used to synthesise a modified form of the classical predictive formula of Kader & Yaglom (Intl J. Heat Mass Transfer, vol. 15 (12), 1972, pp. 2329–2351), which points to some shortcomings of the original formulation. Universality of the mean core scalar profile in defect form is recovered, with very nearly parabolic shape. Logarithmic growth of the buffer-layer peak of the scalar variance is found in the Reynolds number range under scrutiny, which well conforms with Townsend's attached-eddy hypothesis, whose validity is also supported by the spectral maps. The behaviour of the turbulent Prandtl number shows good universality in the outer wall layer, with values $Pr_t \approx 0.84$ , as also found in previous studies, but closer to unity near the wall, where existing correlations do not reproduce the observed trends.

In this study we present a computational model for unprecedented simulations of the left heart in realistic physiological conditions. To this aim, models for the electrical network of contractile muscular fibers (electrophysiology bidomain model), the myocardium mechanics (shells with hyperelastic and orthotropic constitutive relations) and the complex hemodynamics (direct numerical simulation of the Navier–Stokes equations) have been developed and multi-way coupled. The resulting multi-physics model, relying on the immersed-boundary method to cope with the complex fluid–structure interaction, is then validated by replicating the dynamics of the left heart considering simultaneously its atrium and ventricle, with the embedded aortic and mitral valves, and the thoracic aorta where blood is pumped. It is shown that the developed model, when given as input the parameters for the human heart, can reproduce the physiologic velocity and pressure signals obtained by cardiographic diagnostics of real patients.

Direct numerical simulations are employed to reveal three distinctly different flow regions in rotating spherical Rayleigh-B\'enard convection. In the low-latitude region $\mathrm{I}$ vertical (parallel to the axis of rotation) convective columns are generated between the hot inner and the cold outer sphere. The mid-latitude region $\mathrm{II}$ is dominated by vertically aligned convective columns formed between the Northern and Southern hemispheres of the outer sphere. The diffusion-free scaling, which indicates bulk-dominated convection, originates from this mid-latitude region. In the equator region $\mathrm{III}$ the vortices are affected by the outer spherical boundary and are much shorter than in region $\mathrm{II}$. Thermally driven turbulence with background rotation in spherical Rayleigh-B\'enard convection is found to be characterized by three distinctly different flow regions. The diffusion-free scaling, which indicates the heat transfer is bulk-dominated, originates from the mid-latitude region in which vertically aligned vortices are stretched between the Northern and Southern hemispheres of the outer sphere.\ These results show that the flow physics in rotating convection are qualitatively different in planar and spherical geometries. This finding underlines that it is crucial to study convection in spherical geometries to better understand geophysical and astrophysical flow phenomena., Comment: 11pages, 6figures

We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$ , which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$ , which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$ , as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

We analyse the model problem of rigid, spherical pendula impacting on rubber membranes at different Reynolds numbers to understand the contact dynamics in deformable bodies in a viscous fluid. We have investigated the problem both by laboratory and numerical experiments and a new contact model has been developed to perform the simulations. We have found that the collision dynamics depends on many parameters, the most important ones being the impact Stokes number (st) and the ratio of the membrane thickness (e) to sphere diameter (2R). For e/(2R) = 0.1 the pendulum rebounds for st ≥ 18 and this threshold increases as the membrane thickness decreases. Also, the membrane surface affects the dynamics of the impact by delaying the rebound for smaller membranes.

Left ventricle assist devices (VADs) aid the heart pumping blood into the systemic circulation and grant the required cardiac output (CO) when the heart itself cannot provide it. However, it is unclear how effective these devices are at restoring not only physiological CO values but also normal intraventricular hemodynamics. In this work, the modified hemodynamics due to a VAD implantation is studied in vitro using an elastic ventricle made of silicone, which is incorporated into a pulse-duplicator setup prescribing a realistic pulsatile flow. Thereafter, a continuous axial pump is connected at the ventricle apex to mimic a VAD and its effect on the ventricular hemodynamics is investigated as a function of the pump flow suction. Using particle image velocimetry (PIV), we observe that the continuous pump flow effectively provides unloading on the ventricle and yields an increased CO. Conversely, the continuous blood suction from the ventricle apex deeply alters the hemodynamics and, in addition, the VAD obstruction in the ventricle behaves as a bluff body that affects the vorticity distribution in the LV thus creating a stagnant region at the ventricle apex. This phenomenon is rationalized by measuring in a modified set-up the benefits on the hemodynamics of a flush-mounted device. Additionally, the suction operated by the VAD reduces the ventricular pressure and yields an increase in the swirling motion around the ventricle axis, in a similar fashion as the bath-tub vortex effect, thus further modifying the intraventricular hemodynamics with respect to healthy conditions.

In many shear- and pressure-driven wall-bounded turbulent flows secondary motions spontaneously develop and their interaction with the main flow alters the overall large-scale features and transfer properties. Taylor-Couette flow, the fluid motion developing in the gap between two concentric cylinders rotating at different angular velocity, is not an exception, and toroidal Taylor rolls have been observed from the early development of the flow up to the fully turbulent regime. In this manuscript we show that under the generic name of ``Taylor rolls'' there is a wide variety of structures that differ for the vorticity distribution within the cores, the way they are driven and their effects on the mean flow. We relate the rolls at high Reynolds numbers not to centrifugal instabilities, but to a combination of shear and anti-cyclonic rotation, showing that they are preserved in the limit of vanishing curvature and can be better understood as a pinned cycle which shows similar characteristics as the self-sustained process of shear flows. By analyzing the effect of the computational domain size, we show that this pinning is not a product of numerics, and that the position of the rolls is governed by a random process with the space and time variations depending on domain size., Comment: Submitted to JFM

We report on a combined experimental and numerical study of convective heat transfer along ratchet surfaces in vertical natural convection (VC). Due to the asymmetry of the convection system caused by the asymmetric ratchet-like wall roughness, two distinct states exist, with markedly different orientations of the large-scale circulation roll (LSCR) and different heat transport efficiencies. Statistical analysis shows that the heat transport efficiency depends on the strength of the LSCR. When a large-scale wind flows along the ratchets in the direction of their smaller slopes, the convection roll is stronger and the heat transport is larger than the case in which the large-scale wind is directed towards the steeper slope side of the ratchets. Further analysis of the time-averaged temperature profiles indicates that the stronger LSCR in the former case triggers the formation of a secondary vortex inside the roughness cavity, which promotes fluid mixing and results in a higher heat transport efficiency. Remarkably, this result differs from classical Rayleigh–Bénard convection (RBC) with asymmetric ratchets (Jiang et al., Phys. Rev. Lett., vol. 120, 2018, 044501), wherein the heat transfer is stronger when the large-scale wind faces the steeper side of the ratchets. We reveal that the reason for the reversed trend for VC as compared to RBC is that the flow is less turbulent in VC at the same $Ra$. Thus, in VC the heat transport is driven primarily by the coherent LSCR, while in RBC the ejected thermal plumes aided by gravity are the essential carrier of heat. The present work provides opportunities for control of heat transport in engineering and geophysical flows.

In this paper two immersed boundary methods (IBM), specifically a continuous forcing method (CFM) and a discrete forcing method (DFM), are applied to perform direct numerical simulations (DNSs) of heat transfer problems in tubular fluid-particle systems. Both IBM models are built on the well-developed models utilized in momentum transfer studies, and have the capability to handle mixed boundary conditions at the particle surface as encountered in industrial applications with both active and passive particles. Following a thorough verification of both models for the classical Graetz-Nusselt problem, we subsequently apply them to study a much more advanced Graetz-Nusselt problem of more practical importance with a dense stationary array consisting of hundreds of particles randomly positioned inside a tube with adiabatic wall. The influence of particle sizes and fractional amount of passive particles is analyzed at varying Reynolds numbers, and the simulation results are compared between the two IBM models, finding good agreement. Our results thus qualify the two employed IBM modules for more complex applications.

New computational techniques providing more accurate representation of human heart pathologies could help uncovering relevant physical phenomena and improve the outcome of medical therapies. In this framework, the present work describes an efficient computational model for the evaluation of the ventricular flow alteration in presence of mitral valve stenosis. The model is based on the direct numerical simulation of the Navier-Stokes equations two-way coupled with a structural solver for the left ventricle and mitral valve dynamics. The presence of mitral valve stenosis is mimicked by a single-parameter constraint acting on the kinematics of the mitral leaflets. Four different degrees of mitral valve stenosis are considered focusing on the hemodynamic alterations occurring in pathologic conditions. The mitral jet, generated during diastole, is seen to shrink and strengthen when the stenosis gets more severe. As a consequence, the kinetic energy of the flow, the tissues shear stresses, the transvalvular pressure drop and mitral regurgitation increase. It results that, as the stenosis severity level increases, the geometric and effective orifice areas decrease up to 50% with respect the normal case due to the reduced leaflets mobility and stronger blood acceleration during the diastolic phase. The modified intraventricular hemodynamics is also related to a stronger pressure gradient that, for severe stenosis, can be more than ten times larger than the healthy valve case. These computational results are fully consistent with the available clinical literature and open the way to the virtual assessment of surgical procedures and to the evaluation of prosthetic devices.

Solvent exchange is a flow process to induce a transient oversaturation for forming nanobubbles or nanodroplets on solid surfaces by displacing the solution of gases or droplet liquids with a controlled flow of a poor solvent. In this work, we experimentally and numerically investigate the effect of the flow rate and other control parameters on the formation of microbubbles on hydrophobic cavity arrays during the solvent exchange process. We find that the growth rate, location, and number density of microbubbles are closely related to flow rate, solvent concentration, cavity distance, and spatial arrangement. Higher growth rates and number densities of the bubbles were obtained for faster solvent exchange flow rates. The competition of neighbouring growing bubbles for dissolved gas is greatly alleviated when the inter-cavity distance is increased from 13 μ m to 40 μ m. The effects of the flow rate and the cavity spacing on the bubble growth are in agreement with the observations from our three-dimensional numerical simulations. The findings reported in this work provide important insight into the formation of multiple interacting surface microbubbles under various flow conditions. The understanding may be extended to a smaller scale for the growth of surface nanobubbles during solvent exchange, which is much harder to visualize in experiments.