Natural convection of a nanofluid in a square cavity filled with a porous matrix is numerically investigated using a meshless technique. The Darcy–Brinkman and the energy transport equations are used to describe the nanofluid flow and the heat transfer process in the porous medium as these are generated by heating one of the cavity walls. The role of the nanofluid properties in the cooling performance of the medium and in the relevant heat process is thoroughly investigated. Numerical results are obtained for the stream function, the temperature profile, and the Nusselt number over a wide range of dimensionless quantities (Rayleigh number between 10 and 10 , Darcy number between 10 and 10 ). The effect of the porous medium in the cooling efficiency of the nanofluidic system is also discussed. Alternative expressions are suggested for the estimation of the effective conductivity and the thermal expansion coefficient of the nanofluid and their effects on the heat transfer problem are investigated. Excellent agreement with experimental data and trends as well as with previously published numerical results for less complicated systems was found.
In this paper, an analysis is made for the fully developed mixed bioconvection flow in a horizontal channel filled with a nanofluid that contains both nanoparticles and gyrotactic microorganisms. The passively controlled nanofluid model proposed by Kuznetsov and Nield (2013) is then introduced for modeling this flow problem, which is found to be more physically realistic than previous nanofluid models. Analytical approximations with high precision are obtained by the improved homotopy analysis technique for complicated boundary conditions. Besides, the influences of various physical parameters on the distributions of temperature, the nanoparticle volume fraction, as well as the density of motile microorganisms are investigated in detail.
The formation and amplification of streamwise velocity perturbations induced by cross-stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so neatly identified by Ellingsen and Palm in 1975, is a key process in transition to turbulence and self-sustained turbulence. In this review, we first present the original derivation and early studies and then discuss the non-modal growth of streaks, the result of the lift-up process, in transitional and turbulent shear flows. In the second part, the effects on the lift-up process of additives in the fluid and of a second phase are discussed and new results presented with emphasis on particle-laden shear flows. For all cases considered, we see the lift-up process to be a very robust process, always present as a first step in subcritical transition.
Oyster is a surface-piercing flap-type device designed to harvest wave energy in the nearshore environment. Established mathematical theories of wave energy conversion, such as 3D point-absorber and 2D terminator theory, are inadequate to accurately describe the behaviour of Oyster, historically resulting in distorted conclusions regarding the potential of such a concept to harness the power of ocean waves. Accurately reproducing the dynamics of Oyster requires the introduction of a new reference mathematical model, the “flap-type absorber”. A flap-type absorber is a large thin device which extracts energy by pitching about a horizontal axis parallel to the ocean bottom. This paper unravels the mathematics of Oyster as a flap-type absorber. The main goals of this work are to provide a simple–yet accurate–physical interpretation of the laws governing the mechanism of wave power absorption by Oyster and to emphasise why some other, more established, mathematical theories cannot be expected to accurately describe its behaviour.
In this paper, the overall heat transfer coefficient of water based iron oxide nanofluid in a compact air-cooled heat exchanger has been measured experimentally under laminar flow conditions. The concentrations of 0.15, 0.4 and 0.65 vol.% of stabilized Fe O /water nanofluid have been examined with variation of flow rates in the range of 0.2–0.5 m /h. For better dispersion of iron (III) oxide nanoparticles in water, 0.8 wt% polyethylene glycol has been added and pH has been adjusted to 11.1. The air-cooled heat exchanger is consisted of 34 vertical tubes with stadium-shaped cross section and air makes a cross flow through the tube bank with variable flow rates ranging from 740 to 1009 m /h. Also, hot working fluid enters the heat exchanger at different temperatures including 50, 65, and 80 °C. The results demonstrate that increasing the nanofluid flow rate and concentration and the air Reynolds number can improve the overall heat transfer coefficient and heat transfer rate whereas enhancing the inlet temperature has a negative effect on the overall heat transfer coefficient and a positive effect on the heat transfer rate. Meanwhile, the maximum enhancements of the overall heat transfer coefficient and heat transfer rate compared with base fluid (distilled water) are respectively equal to 13% and 11.5% which is occurred at the concentration of 0.65 vol.%.
A recent database from direct numerical simulation (DNS) of a turbulent boundary layer up to (Schlatter and Örlü, 2010) is analysed to extract the dominant flow structures in the near-wall region. In particular, the question of whether hairpin vortices are significant features of near-wall turbulence is addressed. A number of different methods based on the criterion (Jeong and Hussain, 1995) is used to extract turbulent coherent structures: three-dimensional flow visualisation with quantitative estimates of hairpin population, conditional averaging and planar hairpin vortex signatures (HVS). First, visualisations show that during the initial phase of laminar–turbulent transition induced via tripping, hairpin vortices evolving from transitional vortices are numerous and can be considered as the dominant structure of the immediate post-transition stage of the boundary layer. This is in agreement with previous experiments and low-Reynolds-number simulations such as Wu & Moin (2009). When the Reynolds number is increased, the fraction of hairpin vortices decreases to less than 2% for . Second, conditional ensemble averages (Jeong et al., 1997) find hairpins close to the wall at low Reynolds number, while at a sufficient distance downstream from transition, the flow close to the wall is dominated by single quasi-streamwise vortices; even quantitatively, no major differences between boundary layer and channel can be detected. Moreover, three-dimensional visualisations of the neighbourhood of regions of strong swirling motion in planar cuts through the layer (the HVS) do not reveal hairpin vortices, thereby impairing statistical evidences based on HVS. The present results thus clearly confirm that transitional hairpin vortices do not persist in fully developed turbulent boundary layers, and that their dominant appearance as instantaneous flow structures in the outer boundary-layer region is very unlikely.
The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier–Stokes equations. A finite-volume approach with a volume of fluid method is applied to study the Peregrine breather dynamics up to the initial stages of wave breaking. The comparison of the numerical results with laboratory experiments to validate the numerical approach shows very good agreement and suggests that the chosen method is an effective tool to study modulation instability and breather dynamics in water waves with high accuracy even up to the onset of wave breaking. The numerical results also indicate some previously unnoticed characteristics of the flow fields below the water surface of breathers, which might be of significance for short-term prediction of rogue waves. Recurrent wave breaking is also observed.
Fluid flow across a porous cylinder has various engineering applications. In this paper, a two-dimensional, steady, and laminar flow around and through a porous diamond-square cylinder is studied numerically. The governing equations are written for two zones: the clear fluid zone and the porous zone. For the clear fluid zone, the regular Navier–Stokes equation is used; and the Darcy–Brinkman–Forchheimer model is used for simulating flow in the porous zone. The governing equations, together with the relevant boundary conditions, are solved numerically using the finite-volume method (FVM). In this study, the ranges of Reynolds and Darcy numbers are 1–45 and 10 –10 , respectively. The effects of the Darcy and Reynolds numbers on several hydrodynamics parameters such as pressure coefficient, wake structure, and streamlines are explored. Finally, these parameters are compared with the solid and porous diamond-square cylinders. The numerical results indicate that the wake length and pressure coefficient decrease when Darcy number increases.
The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane Couette flow, the flow generated between counter-translating parallel planes. Subcritical here means discontinuous and direct, with strong hysteresis. This is due to the existence of nontrivial flow regimes between the threshold , the upper bound for unconditional return to the base flow, and the threshold characterized by unconditional departure from the base flow. The around is first discussed from an empirical viewpoint (Section ). The recent determination of for pipe flow by Avila et al. (2011) is recalled. Plane Couette flow is next examined. In laboratory conditions, its transitional range displays an oblique pattern made of alternately laminar and turbulent bands, up to a third threshold beyond which turbulence is uniform. Our current theoretical understanding of the problem is next reviewed (Section ): linear theory and non-normal amplification of perturbations; nonlinear approaches and dynamical systems, basin boundaries and chaotic transients in minimal flow units; spatiotemporal chaos in extended systems and the use of concepts from statistical physics, spatiotemporal intermittency and directed percolation, large deviations and extreme values. Two appendices present some recent personal results obtained in plane Couette flow about patterning from numerical simulations and modeling attempts.
In this study, rarefied supersonic and subsonic gas flow around a NACA 0012 airfoil is simulated using both continuum and particle approaches. Navier–Stokes equations subject to the first order slip/jump boundary conditions are solved under the framework of OpenFOAM package. The DSMC solver of the package, i.e., dsmcFoam, has been improved to include a newly presented “simplified Bernoulli trial (SBT)” scheme for inter-molecular collision modeling. The use of SBT collision model permits to obtain accurate results using a much lower number of simulator particles. We considered flow at different angles of attacks and Knudsen numbers at both the subsonic and supersonic regimes. The computed density and surface pressure distributions are compared with the experimental and numerical data and suitable accuracy was observed. We investigate variations of the lift and drag coefficients with the Knudsen number and angle of attack. At low Kn number in supersonic regime, our results for lift coefficient agree well with the linearized theory; however, the deviation starts as soon as the angle of attack goes beyond or shock wave forms above the airfoil. Along with this, we have observed that drag coefficient increases with the Kn number increasing. We also investigated the effect of Kn number on the leading edge shock position and structure, drag polar , and slip velocity over the airfoil.
The instantaneous alignment of the vorticity vector with local principal strain rates is analysed for statistically planar turbulent premixed flames with different values of heat release parameter and global Lewis number spanning different regimes of combustion. It has been shown that the vorticity vector predominantly aligns with the intermediate principal strain rate in turbulent premixed flames, irrespective of the regime of combustion, heat release parameter and Lewis number. However, the relative alignment of vorticity with the most extensive and compressive principal strain rates changes based on the underlying combustion conditions. Detailed physical explanations are provided for the observed behaviours of vorticity alignment with local principal strain rates. It has been shown that heat release due to combustion significantly affects the alignment of vorticity with local principal strain rates. However, the mean contribution of the vortex-stretching term in the transport equation of enstrophy remains positive for all cases considered here, irrespective of the nature of the vorticity alignment.
Study of the secondary vortex ring (SVR) is essential to understand the complicated flow structures of supersonic impulsive jets. In the present study, the main characteristics of compressible secondary vortex ring and the primary vortex ring (PVR) in the starting three-dimensional (3D) flow field of a supersonic underexpanded circular jet are investigated numerically for , 1.4 and 1.8, at a low pressure ratio (jet flow pressure/ambient pressure) of 1.4. The governing equations of large eddy simulation (LES) for compressible flow have been employed and are solved numerically with the combination of high-order hybrid schemes. Our results illustrate the reason for generation of the SVRs by supersonic underexpanded jets, and it is the rolling up of the shear layer which is resulted from the combination of two slip lines when their two triple points on the embedded shock wave interact with each other. After formation, the SVR interacts with the PVR, and rolls over the periphery of PVR and moves upstream. For a higher Mach number of 1.8, multiple SVRs form during the evolution.
The structural sensitivity shows where an instability of a fluid flow is most sensitive to changes in internal feedback mechanisms. It is formed from the overlap of the flow’s direct and adjoint global modes. These global modes are usually calculated with 2D or 3D global stability analyses, which can be very computationally expensive. For weakly non-parallel flows the direct global mode can also be calculated with a local stability analysis, which is orders of magnitude cheaper. In this theoretical paper we show that, if the direct global mode has been calculated with a local analysis, then the adjoint global mode follows at little extra cost. We also show that the maximum of the structural sensitivity is the location at which the local and branches have the same imaginary value. Finally, we use the local analysis to derive the structural sensitivity of two flows: a confined co-flow wake at , for which it works very well, and the flow behind a cylinder at , for which it works reasonably well. As expected, we find that the local analysis becomes less accurate when the flow becomes less parallel.
Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to study the evolution of the wavepackets and the manner in which the parabolized stability equations (PSE) approach models them. An adjoint-based eigenmode decomposition technique is used to project cross-sectional velocity profiles measured using time-resolved particle image velocimetry (PIV) on the different families of eigenmodes present in the LST eigenspectrum. Attention is focused on the evolution of the Kelvin–Helmholtz (K–H) eigenmode and the projection of experimental fluctuations on it, since in subsonic jets the inflectional K–H instability is the only possible mechanism for linear amplification of the large-scale fluctuations, and governs the wavepacket evolution. Comparisons of the fluctuations extracted by projection onto K–H eigenmode with PSE solutions and PIV measurements are made. We show that the jet can be divided into three main regions, classified with respect to the LST eigenspectrum. Near the jet exit, there is significant amplification of the K–H mode; the PSE solution is shown to comprise almost exclusively the K–H mode, and the agreement with experiments shows that the evolution of this mode dominates the near-nozzle fluctuations. For downstream positions, the Kelvin–Helmholtz mode becomes stable and eventually merges with other branches of the eigenspectrum. The comparison between PSE, experiment and the projection onto the K–H mode for downstream positions suggests that the mechanism of saturation and decay of wavepackets is related to a combination of several marginally stable modes, which is reasonably well modeled by linear PSE, but cannot be obtained in the usual application of locally-parallel stability dealing exclusively with the K–H mode. In addition, the projection of empirical data on the K–H eigenmode at a near-nozzle cross-section is shown to be a well-founded method for the determination of the amplitudes of the linear wavepacket models.
The linear instability of several rotating, stably stratified, interior vertical shear flows (U) over bar (z) is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric (U) over bar (z) for intermediate Rossby number (R-0). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate R-0 values and horizontal wavenumbers (k, l) that are far from l = 0 or k = 0, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of A - S = 0 (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178-3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.
The presence of a spiral arterial blood flow pattern in both animals and humans has been widely accepted. The effect of spiral flow on physiological processes associated with abdominal aortic aneurysm (AAA) development and progressions can provide valuable information. The purpose of this study is to investigate the influence of spiral flow on haemodynamic changes in an elastic AAA model by implementing a coupled fluid–structure interaction (FSI) analysis. The results showed that an increase in the intensity of spiral flow resulted in an increase in maximum wall shear stress (WSS) and a decrease in maximum wall stress; however, the spiral flow effect on the WSS was higher than the wall stress. It was also shown that not taking into consideration the effect of spiral flow in modelling of AAA can underestimate the magnitude of WSS by up to 30% and overestimate the magnitude of wall stress by up to 11%. The presence of spiral flow within AAAs is associated with beneficial and detrimental effects. The beneficial effects are to reduce the wall stress and the size of regions with low WSS which in turn reduce the risk of rupture, endothelial dysfunction and the development of atherosclerosis. However, the increase in magnitude of WSS is seen as the detrimental effect of spiral flow.
We formulate a general poromechanics model– within the framework of a two-phase mixture theory– compatible with large strains and without any simplification in the momentum expressions, in particular concerning the fluid flows. The only specific assumptions made are fluid incompressibility and isothermal conditions. Our formulation is based on fundamental physical principles– namely, essential conservation and thermodynamics laws– and we thus obtain a Clausius–Duhem inequality which is crucial for devising compatible constitutive laws. We then propose to model the solid behavior based on a generalized hyperelastic free energy potential– with additional viscous effects– which allows to represent a wide range of mechanical behaviors. The resulting formulation takes the form of a coupled system similar to a fluid–structure interaction problem written in an Arbitrary Lagrangian–Eulerian formalism, with additional volume-distributed interaction forces. We achieve another important objective by identifying the essential energy balance prevailing in the model, and this paves the way for further works on mathematical analyses, and time and space discretizations of the formulation.
In the diffraction of water waves by fixed bodies, the scattered waves propagate outward in the far field and attenuate with increasing distance from the structure. ‘Cloaking’ refers to the reduction in amplitude or complete elimination of the scattered waves. The possibility of cloaking is of both scientific and practical interests. Cloaking is considered here for a circular cylinder on the free surface, surrounded by one or more additional bodies. Linearized time-harmonic motion is assumed. A numerical procedure is used to optimize the geometry of the surrounding bodies, so as to minimize the energy of the scattered waves. Values of the scattered energy are achieved which are practically zero at a specific wavenumber, within the estimated numerical accuracy. This provides tentative support for the existence of perfect cloaking, and conclusive evidence that structures can be designed to have very small values of the mean drift force.