JFM Papers
Internal solitary waves with subsurface cores
- Yangxin He, Kevin G. Lamb, Ren-Chieh Lien
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- Published online by Cambridge University Press:
- 18 June 2019, pp. 1-17
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Large internal solitary waves with subsurface cores have recently been observed in the South China Sea. Here fully nonlinear solutions of the Dubreil–Jacotin–Long equation are used to study the conditions under which such cores exist. We find that the location of the cores, either at the surface or below the surface, is largely determined by the sign of the vorticity of the near-surface background current. The results of a numerical simulation of a two-dimensional shoaling internal solitary wave are presented which illustrate the formation of a subsurface core.
The role of soluble surfactants in the linear stability of two-layer flow in a channel
- A. Kalogirou, M. G. Blyth
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- 18 June 2019, pp. 18-48
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The linear stability of Couette–Poiseuille flow of two superposed fluid layers in a horizontal channel is considered. The lower fluid layer is populated with surfactants that appear either in the form of monomers or micelles and can also get adsorbed at the interface between the fluids. A mathematical model is formulated which combines the Navier–Stokes equations in each fluid layer, convection–diffusion equations for the concentration of monomers (at the interface and in the bulk fluid) and micelles (in the bulk), together with appropriate coupling conditions at the interface. The primary aim of this study is to investigate when the system is unstable to arbitrary wavelength perturbations, and in particular, to determine the influence of surfactant solubility and/or sorption kinetics on the instability. A linear stability analysis is performed and the growth rates are obtained by solving an eigenvalue problem for Stokes flow, both numerically for disturbances of arbitrary wavelength and analytically using long-wave approximations. It is found that the system is stable when the surfactant is sufficiently soluble in the bulk and if the fluid viscosity ratio $m$ and thickness ratio $n$ satisfy the condition $m<n^{2}$. On the other hand, the effect of surfactant solubility is found to be destabilising if $m\geqslant n^{2}$. Both of the aforementioned results are manifested for low bulk concentrations below the critical micelle concentration; however, when the equilibrium bulk concentration is sufficiently high (and above the critical micelle concentration) so that micelles are formed in the bulk fluid, the system is stable if $m<n^{2}$ in all cases examined.
Influence of pitch rate on freely translating perching airfoils
- T. Jardin, N. Doué
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- 20 June 2019, pp. 49-71
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We numerically investigated the unsteady dynamics of a two-dimensional airfoil undergoing a continuous, prescribed pitch-up motion and freely translating as a response to aerodynamic forces and the gravity field. The pitch-up motion was applied about an axis located $1/6$ chord away from the leading edge and was parameterized using the shape change number, with a Reynolds number set to 2000. It was shown that the minimum kinetic energy reached by the airfoil depends stochastically and asymptotically on shape change numbers for values below and above 1, respectively. Very low kinetic energy levels (close to zero) can be reached in both stochastic and asymptotic regions but high shape change numbers are accompanied by significant gain in altitude which may be undesirable from a practical perspective. Rather, shape change numbers in the range [0.1–0.3] allow us to reach relatively low levels of kinetic energy for close perching locations. We showed that highly nonlinear fluid–structure interactions induced by massive flow separations and strong vortices are conducive to low kinetic energy, but responsible for the stochastic dependence of kinetic energy to shape change number, which can make perching manoeuvres hardly controllable for flying vehicles.
Marangoni circulation by UV light modulation on sessile drop for particle agglomeration
- Tianyi Li, Aravinda Kar, Ranganathan Kumar
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- 20 June 2019, pp. 72-88
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An analytical solution of a biharmonic equation is presented in axisymmetric toroidal coordinates for Stokes flow due to surface tension gradient on the free surface of sessile drops. The stream function profiles exhibit clockwise and counter-clockwise toroidal volumes. The ring or dot formed by the downward dividing streamlines between these volumes predicts the experimentally deposited particle ring or dot well. This finding suggests that the downward dividing streamline can be taken to be a reasonable indicator of where deposition occurs. Different light patterns directed at different locations of the droplet can give rise to a single spot or ring. A relationship between the positions of the light intensity peak and possible locations of particle deposition is analysed to demonstrate that the streamlines can be generated on-demand to achieve particle deposition at predetermined locations on the substrate. Toroidal corner vortices called Moffatt eddies have appeared in other corner flows and develop in this optical Marangoni flow as well near the contact line.
Coherent large-scale structures from the linearized Navier–Stokes equations
- Anagha Madhusudanan, Simon. J. Illingworth, Ivan Marusic
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- 20 June 2019, pp. 89-109
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The wall-normal extent of the large-scale structures modelled by the linearized Navier–Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data. A turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=2000$ is considered. We use the two-dimensional (2-D) linear coherence spectrum (LCS) to perform the comparison over a wide range of energy-carrying streamwise and spanwise length scales. The study of the 2-D LCS from DNS indicates the presence of large-scale structures that are coherent over large wall-normal distances and that are self-similar. We find that, with the addition of an eddy viscosity profile, these features of the large-scale structures are captured by the linearized equations, except in the region close to the wall. To further study this coherence, a coherence-based estimation technique, spectral linear stochastic estimation, is used to build linear estimators from the linearized Navier–Stokes equations. The estimator uses the instantaneous streamwise velocity field or the 2-D streamwise energy spectrum at one wall-normal location (obtained from DNS) to predict the same quantity at a different wall-normal location. We find that the addition of an eddy viscosity profile significantly improves the estimation.
Slipping moving contact lines: critical roles of de Gennes’s ‘foot’ in dynamic wetting
- Hsien-Hung Wei, Heng-Kwong Tsao, Kang-Ching Chu
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- 20 June 2019, pp. 110-150
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In the context of dynamic wetting, wall slip is often treated as a microscopic effect for removing viscous stress singularity at a moving contact line. In most drop spreading experiments, however, a considerable amount of slip may occur due to the use of polymer liquids such as silicone oils, which may cause significant deviations from the classical Tanner–de Gennes theory. Here we show that many classical results for complete wetting fluids may no longer hold due to wall slip, depending crucially on the extent of de Gennes’s slipping ‘foot’ to the relevant length scales at both the macroscopic and microscopic levels. At the macroscopic level, we find that for given liquid height $h$ and slip length $\unicode[STIX]{x1D706}$, the apparent dynamic contact angle $\unicode[STIX]{x1D703}_{d}$ can change from Tanner’s law $\unicode[STIX]{x1D703}_{d}\sim Ca^{1/3}$ for $h\gg \unicode[STIX]{x1D706}$ to the strong-slip law $\unicode[STIX]{x1D703}_{d}\sim Ca^{1/2}\,(L/\unicode[STIX]{x1D706})^{1/2}$ for $h\ll \unicode[STIX]{x1D706}$, where $Ca$ is the capillary number and $L$ is the macroscopic length scale. Such a no-slip-to-slip transition occurs at the critical capillary number $Ca^{\ast }\sim (\unicode[STIX]{x1D706}/L)^{3}$, accompanied by the switch of the ‘foot’ of size $\ell _{F}\sim \unicode[STIX]{x1D706}Ca^{-1/3}$ from the inner scale to the outer scale with respect to $L$. A more generalized dynamic contact angle relationship is also derived, capable of unifying Tanner’s law and the strong-slip law under $\unicode[STIX]{x1D706}\ll L/\unicode[STIX]{x1D703}_{d}$. We not only confirm the two distinct wetting laws using many-body dissipative particle dynamics simulations, but also provide a rational account for anomalous departures from Tanner’s law seen in experiments (Chen, J. Colloid Interface Sci., vol. 122, 1988, pp. 60–72; Albrecht et al., Phys. Rev. Lett., vol. 68, 1992, pp. 3192–3195). We also show that even for a common spreading drop with small macroscopic slip, slip effects can still be microscopically strong enough to change the microstructure of the contact line. The structure is identified to consist of a strongly slipping precursor film of length $\ell \sim (a\unicode[STIX]{x1D706})^{1/2}Ca^{-1/2}$ followed by a mesoscopic ‘foot’ of width $\ell _{F}\sim \unicode[STIX]{x1D706}Ca^{-1/3}$ ahead of the macroscopic wedge, where $a$ is the molecular length. It thus turns out that it is the ‘foot’, rather than the film, contributing to the microscopic length in Tanner’s law, in accordance with the experimental data reported by Kavehpour et al. (Phys. Rev. Lett., vol. 91, 2003, 196104) and Ueno et al. (Trans. ASME J. Heat Transfer, vol. 134, 2012, 051008). The advancement of the microscopic contact line is still led by the film whose length can grow as the $1/3$ power of time due to $\ell$, as supported by the experiments of Ueno et al. and Mate (Langmuir, vol. 28, 2012, pp. 16821–16827). The present work demonstrates that the behaviour of a moving contact line can be strongly influenced by wall slip. Such slip-mediated dynamic wetting might also provide an alternative means for probing slippery surfaces.
Wake structure of laminar flow past a sphere under the influence of a transverse magnetic field
- Jun-Hua Pan, Nian-Mei Zhang, Ming-Jiu Ni
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- 20 June 2019, pp. 151-173
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The wake structure of an incompressible, conducting, viscous fluid past an electrically insulating sphere affected by a transverse magnetic field is investigated numerically over flow regimes including steady and unsteady laminar flows at Reynolds numbers up to 300. For a steady axisymmetric flow affected by a transverse magnetic field, the wake structure is deemed to be a double plane symmetric state. For a periodic flow, unsteady vortex shedding is first suppressed and transitions to a steady plane symmetric state and then to a double plane symmetric pattern. Wake structures in the range $210<Re\leqslant 300$ without a magnetic field have a symmetry plane. An angle $\unicode[STIX]{x1D703}$ exists between the orientation of this symmetry plane and the imposed transverse magnetic field. For a given transverse magnetic field, the final wake structure is found to be independent of the initial flow configuration with a different angle $\unicode[STIX]{x1D703}$. However, the orientation of the symmetry plane tends to be perpendicular to the magnetic field, which implies that the transverse magnetic field can control the orientation of the wake structure of a free-moving sphere and change the direction of its horizontal motion by a field–wake–trajectory control mechanism. An interesting ‘reversion phenomenon’ is found, where the wake structure of the sphere at a higher Reynolds number and a certain magnetic interaction parameter ($N$) corresponds to a lower Reynolds number with a lower $N$ value. Furthermore, the drag coefficient is proportional to $N^{2/3}$ for weak magnetic fields or to $N^{1/2}$ for strong magnetic fields, where the threshold value between these two regimes is approximately $N=4$.
Wall-modelled large-eddy simulation of turbulent flow past airfoils
- Wei Gao, Wei Zhang, Wan Cheng, Ravi Samtaney
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- Published online by Cambridge University Press:
- 24 June 2019, pp. 174-210
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We present large-eddy simulation (LES) of flow past different airfoils with $Re_{c}$, based on the free-stream velocity and airfoil chord length, ranging from $10^{4}$ to $2.1\times 10^{6}$. To avoid the challenging resolution requirements of the near-wall region, we develop a virtual wall model in generalized curvilinear coordinates and incorporate the non-equilibrium effects via proper treatment of the momentum equations. It is demonstrated that the wall model dynamically captures the instantaneous skin-friction vector field on arbitrary curved surfaces at the resolved scale. By combining the present wall model with the stretched-vortex subgrid-scale model, we apply the wall-modelled LES approach to three different airfoil cases, spanning different geometrical parameters, different attack angles and low to high $Re_{c}$. The numerical results are verified with direct numerical simulation (DNS) at low $Re_{c}$, and validated with experiment data at higher $Re_{c}$, including typical aerodynamic properties such as pressure coefficient distributions, velocity components and also more challenging measurements such as skin-friction coefficient and Reynolds stresses. All comparisons show reasonable agreement, providing a measure of validity that enables us to further probe simulation results into aspects of flow physics that are not available from experiments. Two techniques to quantify hitherto unexplored physics of flows past airfoils are employed: one is the construction of the anisotropy invariant map, and the second is skin-friction portraits with emphasis on flow transition and unsteady separation along the airfoil surface. The anisotropy maps for all three $Re_{c}$ cases, show clearly that a portion of the flow field is aligned along the axisymmetric expansion line, corresponding to the turbulent boundary layer log-law behaviour and the appearance of turbulent transition. The instantaneous skin-friction portraits reveal a monotonic shrinking of the near wall structure scale. At $Re_{c}=10^{4}$, the interaction between the primary separation bubble and the secondary separation bubble contributes to turbulent transition, similar to the case of flow past a cylinder. At higher $Re_{c}=10^{5}$, the primary separation breaks into several small separation bubbles. At even higher $Re_{c}=2.1\times 10^{6}$, near the turbulent separation, the skin-friction lines show small-scale reversal flows that are similar to those observed in DNS of the flat plate turbulent separation. A notable feature of turbulent separation in flow past an airfoil is the appearance of turbulence structures and small-scale reversal flows in the spanwise direction due to the vortex shedding behaviour.
Large-scale streaky structures in turbulent jets
- Petrônio A. S. Nogueira, André V. G. Cavalieri, Peter Jordan, Vincent Jaunet
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- 24 June 2019, pp. 211-237
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Streaks have been found to be an important part of wall-turbulence dynamics. In this paper, we extend the analysis for unbounded shear flows, in particular a Mach 0.4 round jet, using measurements taken using dual-plane, time-resolved, stereoscopic particle image velocimetry (PIV) taken at pairs of jet cross-sections, allowing the evaluation of the cross-spectral density of streamwise velocity fluctuations resolved into azimuthal Fourier modes. From the streamwise velocity results, two analyses are performed: the evaluation of wavenumber spectra (assuming Taylor’s hypothesis for the streamwise coordinate) and a spectral proper orthogonal decomposition (SPOD) of the velocity field using PIV planes in several axial stations. The methods complement each other, leading to the conclusion that large-scale streaky structures are also present in turbulent jets where they experience large growth in the streamwise direction, energetic structures extending up to eight diameters from the nozzle exit. Leading SPOD modes highlight the large-scale, streaky shape of the structures, whose aspect ratio (streamwise over azimuthal length) is approximately 15. The data were further analysed using SPOD, resolvent and transient growth analyses, good agreement being observed between the models and the leading SPOD mode for the wavenumbers considered. The models also indicate that the lift-up mechanism is active in turbulent jets, with streamwise vortices leading to streaks. The results show that large-scale streaks are a relevant part of the jet dynamics.
Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model
- Nick Pizzo, W. Kendall Melville
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- 24 June 2019, pp. 238-259
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Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrödinger equation of Dysthe (Proc. R. Soc. Lond. A, vol. 369 (1736), 1979, pp. 105–114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of $\unicode[STIX]{x1D716}$ and $\unicode[STIX]{x1D6E5}$, for $\unicode[STIX]{x1D716}$ the linear prediction of the maximum slope at focusing and $\unicode[STIX]{x1D6E5}$ the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of $\unicode[STIX]{x1D716}-\unicode[STIX]{x1D6E5}$ phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air–sea interaction processes is discussed.
Direct numerical simulations of Taylor–Couette turbulence: the effects of sand grain roughness
- Pieter Berghout, Xiaojue Zhu, Daniel Chung, Roberto Verzicco, Richard J. A. M. Stevens, Detlef Lohse
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- 24 June 2019, pp. 260-286
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Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor–Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from $Ta=1.0\times 10^{7}$(corresponding to $Re_{\unicode[STIX]{x1D70F}}=82$) to $Ta=1.0\times 10^{9}$ ($Re_{\unicode[STIX]{x1D70F}}=635$). We focus on the influence of the roughness height $k_{s}^{+}$ in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from $k_{s}^{+}=5$ up to $k_{s}^{+}=92$. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport $Nu_{\unicode[STIX]{x1D714}}$ and by the friction factor $C_{f}$. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness $k_{s}^{+}$ is calculated to be $1.33k$, where $k$ is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (VDI-Forsch., vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer $h_{r}$ with $h_{r}=2.78k_{s}$.
Interaction of coherent flow structures in adverse pressure gradient turbulent boundary layers
- Matthew Bross, Thomas Fuchs, Christian J. Kähler
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- 24 June 2019, pp. 287-321
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With the aim to characterize the near-wall flow structures and their interaction with large-scale motions in the log-law region, time-resolved planar and volumetric flow field measurements were performed in the near-wall and log-law region of an adverse pressure gradient turbulent boundary layer following a zero pressure gradient turbulent boundary layer at a friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}=5000$. Due to the high spatial and temporal resolution of the measurements, it was possible to resolve and identify uniform-momentum zones in the region $z/\unicode[STIX]{x1D6FF}<0.15$ or $z^{+}<350$ and to relate them with well known coherent flow motions near the wall. The space–time results confirm that the turbulent superstructures have a strong impact even on the very near-wall flow motion and also their alternating appearance in time and intensity could be quantified over long time sequences. Using the time record of the velocity field, rare localized separation events appearing in the viscous sublayer were also analysed. By means of volumetric particle tracking velocimetry their three-dimensional topology and dynamics could be resolved. Based on the results, a conceptual model was deduced that explains their rare occurrence, topology and dynamics by means of a complex interaction process between low-momentum turbulent superstructures, near-wall low-speed streaks and tilted longitudinal and spanwise vortices located in the near-wall region.
Bubble and conical forms of vortex breakdown in swirling jets
- Pradeep Moise, Joseph Mathew
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- 24 June 2019, pp. 322-357
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Experimental investigations of laminar swirling jets had revealed a new form of vortex breakdown, named conical vortex breakdown, in addition to the commonly observed bubble form. The present study explores these breakdown states that develop for the Maxworthy profile (a model of swirling jets) at inflow, from streamwise-invariant initial conditions, with direct numerical simulations. For a constant Reynolds number based on jet radius and a centreline velocity of 200, various flow states were observed as the inflow profile’s swirl parameter $S$ (scaled centreline radial derivative of azimuthal velocity) was varied up to 2. At low swirl ($S=1$) a helical mode of azimuthal wavenumber $m=-2$ (co-winding, counter-rotating mode) was observed. A ‘swelling’ appeared at $S=1.38$, and a steady bubble breakdown at $S=1.4$. On further increase to $S=1.5$, a helical, self-excited global mode ($m=+1$, counter-winding and co-rotating) was observed, originating in the bubble’s wake but with little effect on the bubble itself – a bubble vortex breakdown with a spiral tail. Local and global stability analyses revealed this to arise from a linear instability mechanism, distinct from that for the spiral breakdown which has been studied using Grabowski profile (a model of wing-tip vortices). At still higher swirl ($S=1.55$), a pulsating type of bubble breakdown occurred, followed by conical breakdown at 1.6. The latter consists of a large toroidal vortex confined by a radially expanding conical sheet, and a weaker vortex core downstream. For the highest swirls, the sheet was no longer conical, but curved away from the axis as a wide-open breakdown. The applicability of two classical inviscid theories for vortex breakdown – transition to a conjugate state, and the dominance of negative azimuthal vorticity – was assessed for the conical form. As required by the former, the flow transitioned from a supercritical to subcritical state in the vicinity of the stagnation point. The deviations from the predictions of the latter model were considerable.
Viscoelastic liquid curtains: experimental results on the flow of a falling sheet of polymer solution
- A. Gaillard, M. Roché, S. Lerouge, C. Gay, L. Lebon, L. Limat
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- 24 June 2019, pp. 358-409
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We experimentally investigate the extensional flow of a sheet – or curtain – of viscoelastic liquid falling freely from a slot at constant flow rate under gravity. Extruded liquids are aqueous solutions of flexible polyethylene oxide (PEO) and of semi-rigid partially hydrolysed polyacrylamide (HPAM) with low shear viscosities. Velocimetry measurements reveal that the mean velocity field $U(z)$ (where $z$ is the distance from the slot exit) does not reduce to a free fall. More precisely, we show that the liquid falls initially with sub-gravitational accelerations up to a distance from the slot which scales as $g\unicode[STIX]{x1D70F}_{fil}^{2}$ (where $g$ is gravity and $\unicode[STIX]{x1D70F}_{fil}$ is the extensional relaxation time of the liquid) due to the stretching of polymer molecules. Beyond this elastic length, inertia dominates and the local acceleration reaches the asymptotic free-fall value $g$. The length of the sub-gravitational part of the curtain is shown to be much larger than the equivalent viscous length $((4\unicode[STIX]{x1D702}/\unicode[STIX]{x1D70C})^{2}/g)^{1/3}$ for Newtonian liquids of density $\unicode[STIX]{x1D70C}$ and dynamic viscosity $\unicode[STIX]{x1D702}$ which is usually small compared to the curtain length. By analogy with Newtonian curtains, we show that the velocity field $U(z)$ rescales on a master curve. Besides, the flow is shown to be only weakly affected by the history of polymer deformations in the die upstream of the curtain. Furthermore, investigations on the curtain stability reveal that polymer addition reduces the minimum flow rate required to maintain a continuous sheet of liquid.
Turbulent flow of finite-size spherical particles in channels with viscous hyper-elastic walls
- M. N. Ardekani, M. E. Rosti, L. Brandt
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- 24 June 2019, pp. 410-440
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We study single-phase and particle-laden turbulent channel flows bounded by two incompressible hyper-elastic walls with different deformability at bulk Reynolds number $5600$. The solid volume fraction of finite-size neutrally buoyant rigid spherical particles considered is $10\,\%$. The elastic walls are assumed to be of a neo-Hookean material. A fully Eulerian formulation is employed to model the elastic walls together with a direct-forcing immersed boundary method for the coupling between the fluid and the particles. The data show a significant drag increase and the enhancement of the turbulence activity with growing wall elasticity for both the single-phase and particle-laden flows when compared with the single-phase flow over rigid walls. Drag reduction and turbulence attenuation is obtained, on the other hand, with highly elastic walls when comparing the particle-laden flow with the single-phase flow for the same wall properties; the opposite effect, drag increase, is observed upon adding particles to the flow over less elastic walls. This is explained by investigating the near-wall turbulence, where the strong asymmetry in the magnitude of the wall-normal velocity fluctuations (favouring positive $v^{\prime }$), is found to push the particles towards the channel centre. The particle layer close to the wall contributes to turbulence production by increasing the wall-normal velocity fluctuations, so that in the absence of this layer, smaller wall deformations and in turn turbulence attenuation is observed. For a moderate wall elasticity, we increase the particle volume fraction up to $20\,\%$ and find that particle migration away from the wall is the cause of turbulence attenuation with respect to the flow over rigid walls. However, for this higher volume fractions, the particle induced stress compensates for the decreasing Reynolds shear stress, resulting in a higher overall drag for the case with elastic walls. The effect of the wall elasticity on the overall drag reduces significantly with increasing particle volume fraction.
Convection regimes induced by local boundary heating in a liquid–gas system
- Victoria B. Bekezhanova, A. S. Ovcharova
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- 24 June 2019, pp. 441-458
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In the framework of the complete formulation of the conjugate problem, the liquid–gas flow structure arising upon local heating using thermal sources is investigated numerically. The two-layer system is confined by solid impermeable walls. The Navier–Stokes equations in the Boussinesq approximation in the ‘streamfunction–vorticity’ variables are used to describe the media motion. The dynamic conditions at the interface are formulated in terms of the tangential and normal velocities, while the temperature conditions at the external boundaries of the system take into account the presence of local heaters. The influence of the number of heaters and heating modes on the dynamics and character of the appearing convective regimes is analysed. The steady and commutated heating modes for one and two heaters arranged at the lower boundary are investigated. The heating initiates convective and thermocapillary mechanisms causing the fluid motion. Transient regimes with the successive formation of two-vortex, quadruple-vortex and two-vortex flows are observed before the stabilization of the system in the uniform heating mode. A stable thermocapillary deflection appears at the interface above the heater. The commutated mode of heating entails oscillations of the interface with a change in the deflection form and the formation of travelling vortices in the fluids. The impact of particular mechanisms on the flow patterns is analysed. The paper presents typical distributions of the velocity and temperature fields in the system and the position of the interface for the considered cases.
Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures
- Prasad Perlekar
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- 24 June 2019, pp. 459-474
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We conduct direct numerical simulations (DNS) of the Cahn–Hilliard–Navier–Stokes (CHNS) equations to investigate the statistical properties of a turbulent phase-separating symmetric binary-fluid mixture. Turbulence causes an arrest of the phase separation which leads to the formation of a statistically steady emulsion. We characterise turbulent velocity fluctuations in an emulsion for different values of the Reynolds number and the Weber number. Our scale-by-scale kinetic energy budget analysis shows that the interfacial terms in the CHNS equations provide an alternative route for the kinetic energy transfer. By studying the probability distribution function (p.d.f.) of the energy dissipation rate, the vorticity magnitude and the joint-p.d.f. of the velocity-gradient invariants we show that the statistics of the turbulent fluctuations do not change with the Weber number.
The effect of wall-normal gravity on particle-laden near-wall turbulence
- Junghoon Lee, Changhoon Lee
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- 25 June 2019, pp. 475-507
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We performed two-way coupled direct numerical simulations of turbulent channel flow with Lagrangian tracking of small, heavy spheres at a dimensionless gravitational acceleration of 0.077 in wall units, which is based on the flow condition in the experiment by Gerashchenko et al. (J. Fluid Mech., vol. 617, 2008, pp. 255–281). We removed deposited particles after several collisions with the lower wall and then released new particles near the upper wall to observe direct interactions between particles and coherent structures of near-wall turbulence during gravitational settling through the mean shear. The results indicate that when the Stokes number is approximately 1 on the basis of the Kolmogorov time scale of the flow ($St_{K}\approx 1$), the so-called preferential sweeping occurs in association with coherent streamwise vortices, while the effect of crossing trajectories becomes significant for $St_{K}>1$. Consequently, in either case, the settling particles deposit on the wall without strong accumulation in low-speed streaks in the viscous sublayer. When particles settle through near-wall turbulence from the upper wall, more small-scale vortical structures are generated in the outer layer as low-speed fluid is pulled farther in the direction of gravity, while the opposite is true near the lower wall.
Observation of surface wave patterns modified by sub-surface shear currents
- Benjamin K. Smeltzer, Eirik Æsøy, Simen Å. Ellingsen
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- 25 June 2019, pp. 508-530
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We report experimental observations of two canonical surface wave patterns – ship waves and ring waves – skewed by sub-surface shear, thus confirming effects predicted by recent theory. Observed ring waves on a still surface with sub-surface shear current are strikingly asymmetric, an effect of strongly anisotropic wave dispersion. Ship waves for motion across a sub-surface current on a still surface exhibit striking asymmetry about the ship’s line of motion, and large differences in transverse wavelength for upstream versus downstream motion are demonstrated, all of which is in good agreement with theoretical predictions. Neither of these phenomena can occur on a depth-uniform current. A quantitative comparison of measured versus predicted average phase shift for a ring wave is grossly mispredicted by no-shear theory, but in good agreement with predictions for the measured shear current. A clear difference in wave frequency within the ring wave packet is observed in the upstream versus downstream direction for all shear flows, while wave dispersive behaviour is identical to that for quiescent water for propagation normal to the shear current, as expected. Peak values of the measured two-dimensional Fourier spectrum for ship waves are shown to agree well with the predicted criterion of stationary ship waves, with the exception of some cases where results are imperfect due to the limited wavenumber resolution, transient effects and/or experimental noise. Experiments were performed on controlled shear currents created in two different ways, with a curved mesh and beneath a blocked stagnant-surface flow. Velocity profiles were measured with particle image velocimetry, and surface waves with a synthetic schlieren method. Our observations lend strong empirical support to recent predictions that wave forces on vessels and structures can be greatly affected by shear in estuarine and tidal waters.
Rotational stabilisation of the Rayleigh–Taylor instability at the inner surface of an imploding liquid shell
- Justin Huneault, David Plant, Andrew J. Higgins
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- 25 June 2019, pp. 531-567
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A number of applications utilise the energy focussing potential of imploding shells to dynamically compress matter or magnetic fields, including magnetised target fusion schemes in which a plasma is compressed by the collapse of a liquid metal surface. This paper examines the effect of fluid rotation on the Rayleigh–Taylor (RT) driven growth of perturbations at the inner surface of an imploding cylindrical liquid shell which compresses a gas-filled cavity. The shell was formed by rotating water such that it was in solid body rotation prior to the piston-driven implosion, which was propelled by a modest external gas pressure. The fast rise in pressure in the gas-filled cavity at the point of maximum convergence results in an RT unstable configuration where the cavity surface accelerates in the direction of the density gradient at the gas–liquid interface. The experimental arrangement allowed for visualisation of the cavity surface during the implosion using high-speed videography, while offering the possibility to provide geometrically similar implosions over a wide range of initial angular velocities such that the effect of rotation on the interface stability could be quantified. A model developed for the growth of perturbations on the inner surface of a rotating shell indicated that the RT instability may be suppressed by rotating the liquid shell at a sufficient angular velocity so that the net surface acceleration remains opposite to the interface density gradient throughout the implosion. Rotational stabilisation of high-mode-number perturbation growth was examined by collapsing nominally smooth cavities and demonstrating the suppression of small spray-like perturbations that otherwise appear on RT unstable cavity surfaces. Experiments observing the evolution of low-mode-number perturbations, prescribed using a mode-6 obstacle plate, showed that the RT-driven growth was suppressed by rotation, while geometric growth remained present along with significant nonlinear distortion of the perturbations near final convergence.