Latest papers in fluid mechanics
A peeling bubble of air propagates when a newborn breathes for the first time. In experimental conditions, peeling fingers are unstable depending on the cross-sectional area and capillary thresholds. In this work, the deformation of a thin elastic membrane on top of a channel and its interaction with the boundary layer/solid plate yields interface wavenumbers in agreement with K41 theory defining inertial, turbulent, and dissipative regimes. Three-dimensional solutions of the minimal set of equations at the low stiffness and low capillary ranges yield symmetric round-type bubbles in numerical simulations. The mechanism responsible for the increase/decrease in the air bubble speed at large time scales is related to the wetting ridge gradient developed around the finger that defines two sorts of propagation: (i) the speed of the bubble decreases transferring energy to the membrane–fluid interface and (ii) the air finger increases its speed as it obtains energy from the elastic membrane and fluid layer, decreasing their temperature. The menisci at the bubble–liquid–shell interface are triggered by elastic and capillary forces that deform the interface around the finger, and the scale of these ridges is of the order of the elastocapillary length.
Energy budget analysis and neutral curve characteristics for the linear instability of Couette–Poiseuille flow
Here, we present some interesting new results on the linear modal stability of the Couette–Poiseuille flow (CPF), by numerically solving the Orr–Sommerfeld equation within the temporal framework. We provide a mechanistic explanation to the well-known result that the upper plate movement causes progressive stabilization of the CPF. The temporal energy budget reveals appearance of a region of negative energy production with plate movement, which is located near the plate that has a higher relative velocity in the direction of the bulk flow. This has a negative contribution to the integral production term, which, along with the expectation that energy dissipation is nominally constant (to leading order) at a given Reynolds number (Re), reduces the growth rate of kinetic energy, thereby causing flow stabilization with an increase in plate speed. Next, we compare the linear stability portrait of the CPF for positive and negative plate speeds and find that the upper and lower neutral branches in the frequency-Re plane cross over each other (to form a “loop”) for a certain range of negative plate speeds. Interestingly, this behavior is not seen for positive plate speeds. At high Re and small plate speeds (positive/negative), we observe that the CPF supports an additional unstable mode manifested in the neutral curves as a bifurcation of the unstable region into primary and secondary regions. The secondary unstable mode is found to be sufficiently distinct in character from the primary mode. These results contribute to the contemporary efforts to better understand the stability of the CPF.
Owing to the lack of consensus about the way Chapman–Enskog should be performed, a new Taylor-expansion of lattice-Boltzmann models is proposed. In contrast to the Chapman–Enskog expansion, recalled in this manuscript, the method only assumes a sufficiently small time step. Based on the Taylor expansion, the collision kernel is reinterpreted as a closure for the stress-tensor equation. Numerical coupling of lattice-Boltzmann models with other numerical schemes, also encompassed by the method, is shown to create error terms whose scalings are more complex than those obtained via Chapman–Enskog. An athermal model and two compressible models are carefully analyzed through this new scope, casting a new light on each model's consistency with the Navier–Stokes equations.
In this paper, the simplified discrete unified gas-kinetic scheme presented in the former paper is extended from incompressible flow to compressible flow at a high Mach number. In our earlier work, a simplified discrete unified gas–kinetic scheme was developed for low-speed flow in which the Mach number is small for keeping the incompressible property. To simulate compressible flow, the governing equation of the internal energy distribution function presented as potential energy including the Prandtl number effect is introduced to the present method. The velocity field is coupled with density and internal energy by the evolution of distribution functions related to mass, momentum, and temperature. For simplification and computational efficiency, the D2Q13 circular distribution function is applied as the equilibrium model. Compared to our earlier work, higher Mach number flows can be simulated by the proposed method, which is of the ability to simulate compressible flow. A number of numerical test cases from incompressible to compressible flows have been conducted, including incompressible lid-driven cavity flow, Taylor vortex flow, transonic flow past NACA (National Advisory Committee for Aeronautics) 0012 airfoil, Sod shock tube, supersonic flow past a circular cylinder, and isentropic vortex convection. All simulation results agree well with the reference data.
Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damköhler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames. At low Karlovitz numbers, where heat-release effects dominate turbulent kinetic energy budgets, their relative significance scales with the integral Damköhler number in a priori Reynolds-Averaged Navier–Stokes (RANS) statistics and the filter Damköhler number in Large Eddy Simulation (LES). The Damköhler-number scaling of counter-gradient transport in this regime follows theoretical arguments underpinning linear-algebraic turbulence models, which explains their efficacy at low Karlovitz numbers. Conversely, at moderate Karlovitz numbers, LES subfilter turbulence is more strongly influenced by heat-release effects than the analogous large-scale RANS turbulence. This is consistent with the notion of an “active cascade,” which postulates that heat-release-induced volumetric expansion competes on intermediate scales with classical forward-cascade energy transfer. LES exposes these dynamics as dominant subfilter-scale physics, unlike in RANS, where they are secondary to the effects of mean-shear production at the large scales. The significance of subfilter-scale interactions is promoted by the LES filter itself, which modifies the RANS spectral basis by incorporating local flame-normal averaging. This is highlighted by comparing LES fields obtained using a 3D filter to those using a modified 2D filter, excluding the flame-normal direction, which significantly reduces the apparent influence of heat-release effects but is not representative of LES in practice. The subfilter modeling challenges posed by these distinctions at moderate Karlovitz numbers and order-unity Damköhler numbers remain to be understood.
The responses to external excitations in thermocapillary liquid layers are investigated by non-modal stability theory. The maximum amplification of input signals is measured by a response function depending on the perturbation velocity and temperature. There can be rather large amplifications in subcritical flows at both small and large Prandtl numbers (Pr). For small Pr, the response increases significantly with both the Reynolds number (R) and the Biot number (Bi) but decreases with Pr. The optimal response is achieved when the perturbation is almost a spanwise wave. The response properties for the linear flow and the return flow are similar. The amplification is caused by a combination of the lift-up mechanism, Orr mechanism, and external forcing. However, for large Pr, large amplifications could only be found in the return flow, while the variations of response with Pr and Bi are opposite to those at small Pr. The optimal response propagates in the streamwise direction. The amplification is caused by the thermocapillary effect.
Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data
We evaluate a number of different finite-element approaches for fluid–structure (contact) interaction problems against data from physical experiments. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change in the fluid domain and the contact between the wall and the particle. In the finite-element simulations, we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare the results obtained with the well-established Arbitrary Lagrangian–Eulerian (ALE) approach and an unfitted moving domain method together with a simple and common approach for contact avoidance. For the full fluid–structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency, we use the geometrical symmetry of the experimental setup to reformulate the FSI system into two spatial dimensions. Finally, we show full three-dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries, and the results are made freely available to aid reproducibility.
The impact of periodic pulsation normal to the flow passage on the heat and momentum transport is studied using direct numerical simulations. The selected test case is the fully developed supersonic turbulent flow at Reynolds numbers [math] and 6000 and Mach number [math], bounded by isothermal walls. The pulsation is introduced by imposing a time-periodic uniform body-force in the spanwise directions, mimicking two acoustic drivers placed on the side-walls that are operating with a 180° phase difference. Results indicate that the spanwise pulsation at a moderate forcing amplitude, with the spanwise velocity oscillation amplitude [math] of bulk streamwise velocity or [math], can create about 8% reduction in the Nusselt number (Nu), as well as in the skin friction coefficient (Cf), if applied at the optimal pulsation period [math] within [173, 346], where [math]. The excitation outside this band fails to achieve such high levels of modulations in heat and momentum transport processes near the walls. Visualizing the instantaneous temperature field reveals a periodic tilting of the near-wall turbulent structures that is translated into a decay in the energy of the streamwise vortices and an increase in the mean spanwise distance of such structures. The effect of the excitation on reducing the turbulent heat flux and Reynolds shear stress is studied, and the resulting streaming temperature and velocity profiles are discussed.
The incompressible flow of a Maxwell fluid through a curved duct with a rectangular cross section is numerically investigated over a wide range of the Dean number and curvature of the duct. Unsteady solutions, such as periodic, multi-periodic, and chaotic solutions, are obtained by using the spectral method. The combined effects of the large Dean number, Deborah number, and curvature on fluid flow behaviors are discussed in detail. It is found that increasing the Deborah number accelerates the occurrence of the four-cell structure of secondary flow no matter what the Dean number is. Periodic solutions are found to appear for the case of a smaller Dean number due to the presence of elasticity. The periodic solution turns to a chaotic solution if the Dean number is further increased. The chaotic solution is weak for a smaller Deborah number, while it becomes strong for a larger Deborah number. In addition, time evolution calculations at Dn = 300 show that the flow state changes significantly if the curvature δ is increased to be the critical value of the curvature δc = 0.26, while it remains almost unchanged for δ > δc or δ < δc.
Numerical study of equilibrium radial positions of neutrally buoyant balls in circular Poiseuille flows
In this article, we have studied, via direct numerical simulations, the equilibrium radial positions of neutrally buoyant balls moving in circular Poiseuille flows. For the one ball case, the Segre–Silberberg effect takes place at low Reynolds numbers (Re) as expected. However, at higher Re, the ball moves to one of two equilibrium positions. At even higher Re, the ball is pinched to a radial position closer to the central axis. For the case of two neutrally buoyant balls placed on a line parallel with the central axis initially, this two-ball train is stable at low Re and its mass center moves to the outer Segre–Silberberg equilibrium position like the migration of a single neutrally buoyant ball. Moreover, for Re values greater than the critical value, Rec = 435, the two-ball train is unstable. The two balls interact periodically, suggesting a (kind of) Hopf bifurcation phenomenon. Nevertheless, the averaged mass center of the two balls is located at the inner equilibrium radial position.
Motivated by the recent discovery of a dispersive-to-nondispersive transition for linear waves in shear flows, we accurately explored the wavenumber-Reynolds number parameter map of the plane Poiseuille flow in the limit of least-damped waves. We have discovered the existence of regions of the map where the dispersion and propagation features vary significantly from their surroundings. These regions are nested in the dispersive, low-wavenumber part of the map. This complex dispersion scenario demonstrates the existence of linear dispersive focusing in wave envelopes evolving out of an initial, spatially localized, three-dimensional perturbation. An asymptotic wave packet's representation, based on the saddle-point method, allows to enlighten the nature of the packet's morphology, in particular, the arrow-shaped structure and spatial spreading rates. A correlation is also highlighted between the regions of largest dispersive focusing and the regions which are most subject to strong nonlinear coupling in observations.
Turbulent scalar fluxes from a generalized Langevin model: Implications on mean scalar mixing and tracer particle dispersion
A Generalized Langevin Model (GLM) formulation to be used in transported joint velocity-scalar probability density function methods is recalled in order to imply a turbulent scalar-flux model where the pressure-scrambling term is in correspondence with standard Monin's return-to-isotropy term. The proposed non-constant C0 formulation is extended to seen-velocity models for particle dispersion modeling in dispersed two-phase flows. This allows us to correct the wrong turbulent scalar-flux modeling in the limit of tracer particles. Moreover, this allows us to have a more general formulation in order to consider advanced Reynolds-stress models. The cubic model of Fu, Launder, and Tselepidakis is considered, together with the model of Merci and Dick for turbulent dissipation. Results are presented for different swirling and recirculating single-phase and two-phase flows, showing the capabilities of the proposed non-constant C0 GLM formulations compared to the standard GLM.
A practical simulation of a hexanitrohexaazaisowurtzitane (CL-20) sphere detonated underwater with the Taylor wave solution and modified Tait parameters
The modified ghost fluid method (MGFM) has been one of the most popular and successful algorithms for coping with the numerical calculation of multi-medium flows, especially for the interaction between strong discontinuities and material interfaces. To apply the advanced algorithm to an underwater explosion simulation, first, the uniform distribution of the state of the detonation products, which is the most generally used initial condition in an explosion simulation, is replaced by the analytic solution of the Taylor wave. The Tait equation is, then, expanded to a broader pressure coverage of up to 100 GPa to match the initial state at the discontinuity. One-dimensional Euler equations with source terms governing the explosion flow are discretized with the fifth-order weighted essentially non-oscillatory scheme in space and the third-order Runge–Kutta scheme in time. The gas–water interface is tracked with the level set equations, and the intermediate states are resolved and defined by following the MGFM. In addition to the comparative studies among diverse numerical cases, experimental data were offered as a calibration in this work. The temporal and spatial distribution characteristics of the energy and flow variables were comprehensively discussed. Studies and analysis showed that (1) the novelly achieved parameters B = 710.8 MPa and γ = 5.22 for the Tait equation of state were highly recommended for any application involving transient loads. (2) The explosion flow field produced by the Taylor wave model was closer to the nature of physical reality. (3) Without considering the details, the stationary wave model was not entirely unacceptable as an initial condition for roughly simulating an explosion effect. The most important thing was that one had to ensure that the initial energy was equivalent to the Taylor wave case.
The mutual coupling effect between the fluid flow and the in situ stress fields cannot be ignored during the development of natural fractured reservoirs (NFRs), such as in the waterflooding process. In this study, a discrete fracture model is proposed to simulate the rock deformation and two-phase flow behaviors of oil and water in the NFR. The numerical solution of the model is achieved via the finite-element method and control-volume finite-element method. The numerical simulator is verified using commercial software, and a perfect agreement is obtained. Finally, sensitivity analysis is conducted on the key parameters in the model, such as fracture parameters, matrix permeability, and injection intensity. Results show that the fluid–solid coupling effect gradually weakens with production time. The degree of the fluid–solid coupling on cumulative oil production becomes smaller as the permeability of the matrix increases. Fracture connectivity controls the velocity and direction of the water flood front. Water injection intensity directly affects the natural fracture opening deformation and well productivity. The research and the numerical results obtained in this paper can provide theoretical guidance for the optimal design of water flooding operations in NFR.
Limit of the buoyancy ratio in Boussinesq approximation for double-diffusive convection in binary mixture
This paper deals with a mathematical and numerical investigation of double-diffusive natural convective heat and mass transfer in a cavity filled with Newtonian fluid with significant density and mass diffusivity changes. In such a situation, the assumption of the Boussinesq approximation is not justified, and an appropriate model based on a set of Low Mach Number equations is used. The active parts of two vertical walls of the cavity are maintained at fixed but different temperatures and concentrations, while the other two walls, as well as inactive areas of the sidewalls, are considered to be adiabatic and impermeable to mass transfer. The coupled momentum, energy, and solute transfer equations in binary mixtures of ideal gases are solved through a global iterative procedure based on the finite volume methods in the context of the low Mach number approximation. The study includes the effect of the buoyancy ratio N with the aim to find its application limit in the Boussinesq conditions. The results show that if we use the Boussinesq approximation to study double-diffusive convection, the value of parameter N must be between −6 and 27.
This Letter reports the first large eddy simulation of a turbulent flame using a lattice-Boltzmann model. To that end, simulation of a bluff-body stabilized propane–air flame is carried out, showing an agreement similar to those available in the literature. Computational costs are also reported, indicating that lattice-Boltzmann modeling of reactive flows is competitive, with around 1000cpuh required to simulate one residence time in the 1.5 m burner.
The destabilization of emulsions is important for many applications but remains incompletely understood. We perform squeeze flow measurements on oil-in-water emulsions, finding that the spontaneous destabilization of emulsions is generally very slow under normal conditions, with a characteristic time scale given by the drainage of the continuous phase and the coalescence of the dispersed phase. We show that if the emulsion is compressed between two plates, the destabilization can be sped up significantly; on the one hand, the drainage is faster due to the application of the squeezing force. On the other hand, creep processes lead to rearrangements that also contribute to the destabilization.
A three-dimensional physical and mathematical model of the lateral airflow for droplet breakup was established. Numerical simulation was used to study the impact of the pulsating airflow on the droplet breakup process and analyze the variation in deformation rate under different amplitudes and frequencies. The results show that compared with uniform airflow, pulsating airflow can enhance the effect of droplet breakup, with an optimal droplet crushing effect occurring when the relative amplitude of the pulsating airflow was A = 1 and the Womersley number of the pulsating airflow was 96.6.
Author(s): R. Kree, L. Rückert, and A. Zippelius
A most important challenge on the way towards reliable biotechnological systems is to find biocompatible, long lasting, and precisely controllable methods of propulsion in vivo. In the present theoretical work we explore possibilities of actuating a soft droplet by small internal motors, which either operate autonomously, or are externally driven, or both. Motors and external drives are modeled as point forces.
[Phys. Rev. Fluids 6, 034201] Published Mon Mar 01, 2021
Data-driven subgrid-scale modeling of forced Burgers turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning
Developing data-driven subgrid-scale (SGS) models for large eddy simulations (LESs) has received substantial attention recently. Despite some success, particularly in a priori (offline) tests, challenges have been identified that include numerical instabilities in a posteriori (online) tests and generalization (i.e., extrapolation) of trained data-driven SGS models, for example, to higher Reynolds numbers. Here, using the stochastically forced Burgers turbulence as the test-bed, we show that deep neural networks trained using properly pre-conditioned (augmented) data yield stable and accurate a posteriori LES models. Furthermore, we show that transfer learning enables accurate/stable generalization to a flow with [math] higher Reynolds number.