Showing papers on "Incompressible flow published in 2015"

Divergence-free smoothed particle hydrodynamics

Abstract: In this paper we introduce an efficient and stable implicit SPH method for the physically-based simulation of incompressible fluids. In the area of computer graphics the most efficient SPH approaches focus solely on the correction of the density error to prevent volume compression. However, the continuity equation for incompressible flow also demands a divergence-free velocity field which is neglected by most methods. Although a few methods consider velocity divergence, they are either slow or have a perceivable density fluctuation.Our novel method uses an efficient combination of two pressure solvers which enforce low volume compression (below 0.01%) and a divergence-free velocity field. This can be seen as enforcing incompressibility both on position level and velocity level. The first part is essential for realistic physical behavior while the divergence-free state increases the stability significantly and reduces the number of solver iterations. Moreover, it allows larger time steps which yields a considerable performance gain since particle neighborhoods have to be updated less frequently. Therefore, our divergence-free SPH (DFSPH) approach is significantly faster and more stable than current state-of-the-art SPH methods for incompressible fluids. We demonstrate this in simulations with millions of fast moving particles.

The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces

Abstract: A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface. The model is compared to solutions of the full Euler equations for compressible two phase flow, using numerical solutions based on the method of front tracking. The front tracking method has the distinguishing feature of being a predominantly Eulerian method in which sharp interfaces are preserved with zero numerical diffusion. Various regimes in the statistical model exhibiting qualitatively distinct behavior are explored.

The time-resolved natural flow field of a fluidic oscillator

Abstract: The internal and external flow field of a fluidic oscillator with two feedback channels are examined experimentally within the incompressible flow regime. A scaled-up device with a square outlet nozzle is supplied with pressurized air and emits a spatially oscillating jet into quiescent environment. Time-resolved information are obtained by phase-averaging pressure and PIV data based on an internal reference signal. The temporal resolution is better than a phase angle of 3°. A detailed analysis of the internal dynamics reveals that the oscillation mechanism is based on fluid feeding into a separation bubble between the jet and mixing chamber wall which pushes the jet to the opposite side. The total volume of fluid transported through one feedback channel during one oscillation cycle matches the total growth of the separation bubble from its initial size to its maximum extent. Although the oscillation frequency increases linearly with supply rate, sudden changes in the internal dynamics are observed. These changes are caused by a growth in reversed flow through the feedback channels. The time-resolved properties of the emitted jet such as instantaneous jet width and exit velocity are found to oscillate substantially during one oscillation cycle. Furthermore, the results infer that the jet’s oscillation pattern is approximately sinusoidal with comparable residence and switching times.

Critical phenomenon of the order–disorder transition in incompressible active fluids

Abstract: We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is discontinuous, in incompressible systems this transition can be continuous, and belongs to a new universality class. We calculate the critical exponents to in an expansion, and derive two exact scaling relations. This is the first analytic treatment of a phase transition in a new universality class in an active system.

Depth-averaged analytic solutions for free-surface granular flows impacting rigid walls down inclines.

Abstract: In the present paper, flows of granular materials impacting wall-like obstacles down inclines are described by depth-averaged analytic solutions. Particular attention is paid to extending the existing depth-averaged equations initially developed for frictionless and incompressible fluids down a horizontal plane. The effects of the gravitational acceleration along the slope, and of the retarding acceleration caused by friction as well, are systematically taken into account. The analytic solutions are then used to revisit existing data on rigid walls impacted by granular flows. This approach allows establishing a complete phase diagram for granular flow-wall interaction.

The Interplay of Curvature and Vortices in Flow on Curved Surfaces

Abstract: Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry, and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements. Motivated by designed examples for superfluids, we numerically consider the influence of a geometric potential on vortices for fluids with finite viscosity and show examples in which a change in the geometry is used to manipulate the flow field.

Global well-posedness of an initial-boundary value problem for viscous non-resistive MHD systems

Abstract: This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and (nonhomogeneous and homogeneous) incompressible fluids in an infinite flat layer. We prove the global well-posedness of the systems around a uniform magnetic field which is vertical to the layer. Moreover, the solution converges to the steady state at an almost exponential rate as time goes to infinity. Our proof relies on a two-tier energy method for the reformulated systems in Lagrangian coordinates.

Model-reduced variational fluid simulation

Abstract: We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the simplicity of sub-grid accurate boundary conditions on regular grids to deal with arbitrarily-shaped domains. At the core of our contributions is a functional map approach to fluid simulation for which scalar- and vector-valued eigenfunctions of the Laplacian operator can be easily used as reduced bases. Using a variational integrator in time to preserve liveliness and a simple, yet accurate embedding of the fluid domain onto a Cartesian grid, our model-reduced fluid simulator can achieve realistic animations in significantly less computational time than full-scale non-dissipative methods but without the numerical viscosity from which current reduced methods suffer. We also demonstrate the versatility of our approach by showing how it easily extends to magnetohydrodynamics and turbulence modeling in 2D, 3D and curved domains.

Theoretical analysis of slip flow on a rotating cone with viscous dissipation effects

Abstract: This paper is concerned with the mutual effects of viscous dissipation and slip effects on a rotating vertical cone in a viscous fluid. Similarity solutions for rotating cone with wall temperature boundary conditions provides a system of nonlinear ordinary differential equations which have been treated by optimal homotopy analysis method (OHAM). The obtained analytical results in comparison with the numerical ones show a noteworthy accuracy for a special case. Effects for the velocities and temperature are revealed graphically and the tabulated values of the surface shear stresses and the heat transfer rate are entered in tables. From the study it is seen that the slip parameter γ enhances the primary velocity while the secondary velocity reduces. Further it is observed that the heat transfer rate NuRe x −½ increases with Eckert number Ec and Prandtl number Pr.

A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast

Abstract: A hybrid phase field multiple relaxation time lattice Boltzmann method (LBM) is presented in this paper for simulation of multiphase flows with large density contrast. In the present method, the flow field is solved by a lattice Boltzmann equation. Concurrently, the interface of two fluids is captured by solving the macroscopic Cahn-Hilliard equation using the upwind scheme. To be specific, for simulation of the flow field, an lattice Boltzmann equation (LBE) model developed in Shao et al. (Physical Review E, 89 (2014), 033309) for consideration of density contrast in the momentum equation is used. Moreover, in the present work, the multiple relaxation time collision operator is applied to this LBE to enable simulation of problems with large viscosity contrast or high Reynolds number. For the interface capturing, instead of solving another set of LBE as in many phase field LBMs, the macroscopic Cahn-Hilliard equation is directly solved by using a weighted essentially non-oscillatory scheme. In this way, the present hybrid phase field LBM shares full advantages of the phase field LBM while enhancing numerical stability. The ability of the present method to simulate multiphase flow problems with large density contrast is demonstrated by several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

Abstract: The viscous and inviscid linear stability of the incompressible flow past a square open cavity is studied numerically. The analysis shows that the flow first undergoes a steady three-dimensional bifurcation at a critical Reynolds number of 1370. The critical mode is localized inside the cavity and has a flat roll structure with a spanwise wavelength of about 0.47 cavity depths. The adjoint global mode reveals that the instability is most efficiently triggered in the thin region close to the upstream tip of the cavity. The structural sensitivity analysis identifies the wavemaker as the region located inside the cavity and spatially concentrated around a closed orbit. As the flow outside the cavity plays no role in the generation mechanisms leading to the bifurcation, we confirm that an appropriate parameter to describe the critical conditions in open cavity flows is the Reynolds number based on the average velocity between the two upper edges. Stabilization is achieved by a decrease of the total momentum inside the shear layer that drives the core vortex within the cavity. The mechanism of instability is then studied by means of a short-wavelength approximation considering pressureless inviscid modes. The closed streamline related to the maximum inviscid growth rate is found to be the same as that around which the global wavemaker is concentrated. The structural sensitivity field based on direct and adjoint eigenmodes, computed at a Reynolds number far higher than that of the base flow, can predict the critical orbit on which the main instabilities inside the cavity arise. Further, we show that the sub-leading unstable time-dependent modes emerging at supercritical conditions are characterized by a period that is a multiple of the revolution time of Lagrangian particles along the orbit of maximum growth rate. The eigenfrequencies of these modes, computed by global stability analysis, are in very good agreement with the asymptotic results.

Local projection FEM stabilization for the time-dependent incompressible Navier–Stokes problem

Abstract: We consider conforming finite element (FE) approximations of the timedependent, incompressible Navier-Stokes problem with inf-sup stable approximation of velocity and pressure. In case of high Reynolds numbers, a local projection stabilization (LPS) method is considered. In particular, the idea of streamline upwinding is combined with stabilization of the divergence-free constraint. For the arising nonlinear semidiscrete problem a stability and convergence analysis is given. Our approach improves some results of a recent paper by Matthies/Tobiska [1] for the linearized model and takes partly advantage of the analysis in [2] for edge-stabilized FE approximation of the Navier-Stokes problem. Some numerical experiments complement the theoretical results. October 16, 2014

Investigation of Different Droplet Formation Regimes in a T-junction Microchannel Using the VOF Technique in OpenFOAM

Abstract: Here we aimed to investigate various droplet formation regimes in a two-dimensional T-junction microchannel geometry using the open source software OpenFOAM. Two incompressible fluids, continuous phase in the main channel and dispersed phase in the lateral channel, have been considered. The interFoam solver was used to simulate laminar flow with two incompressible and isothermal phases. We evaluated the capability of “Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM)” volume of fluid (VOF) technique of the OpenFOAM for modeling of the droplet formation and movement in different regimes. The flow behavior in the T-junction microchannel over a wide range of capillary numbers (0.006 to 0.12), volume flow rate ratio (0.125, 0.25, 0.5), and contact angle (130° to 180°) in the squeezing, dripping and jetting regimes were examined.The importance of parameters such as contact angle, capillary number, flow rate ratio, and Reynolds number at the time of separation, as well as the formation of droplets, was investigated in different regimes. We found that droplet detachment time increases by increasing the contact angle in the squeezing regime while increasing the contact angle in the dripping regime results in a decrease in the droplet detachment time. We compare the role of pressure gradient and shear stress forces in the droplet formation process in both dripping and squeezing regimes in details. We also provide a classification of two-phase flow regimes in the investigated T-junction microchannel in terms of three main parameters of, e.g., flow rate ratio, contact angle, and capillary number.

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

Abstract: Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

Nonlinear optimal suppression of vortex shedding from a circular cylinder

Abstract: This study is focused on two- and three-dimensional incompressible flow past a circular cylinder for Reynolds number Re⩽1000. To gain insight into the mechanisms underlying the suppression of unsteadiness for this flow we determine the nonlinear optimal open-loop control driven by surface-normal wall transpiration. The spanwise-constant wall transpiration is allowed to oscillate in time, although steady forcing is determined to be most effective. At low levels of control cost, defined as the square integration of the control, the sensitivity of unsteadiness with respect to wall transpiration is a good approximation of the optimal control. The distribution of this sensitivity suggests that the optimal control at small magnitude is achieved by applying suction upstream of the upper and lower separation points and blowing at the trailing edge. At high levels of wall transpiration, the assumptions underlying the linearized sensitivity calculation become invalid since the base flow is eventually altered by the size of the control forcing. The large-magnitude optimal control is observed to spread downstream of the separation point and draw the shear layer separation towards the rear of the cylinder through suction, while blowing along the centreline eliminates the recirculation bubble in the wake. We further demonstrate that it is possible to completely suppress vortex shedding in two- and three-dimensional flow past a circular cylinder up to Re=1000, accompanied by 70 % drag reduction when a nonlinear optimal control of moderate magnitude (with root-mean-square value 8 % of the free-stream velocity) is applied. This is confirmed through linearized stability analysis about the steady-state solution when the nonlinear optimal wall transpiration is applied. While continuously distributed wall transpiration is not physically realizable, the study highlights localized regions where discrete control strategies could be further developed. It also highlights the appropriate range of application of linear and nonlinear optimal control to this type of flow problem.

The Effect of Thermophoresis on Unsteady Oldroyd-B Nanofluid Flow over Stretching Surface

Abstract: There are currently only a few theoretical studies on convective heat transfer in polymer nanocomposites. In this paper, the unsteady incompressible flow of a polymer nanocomposite represented by an Oldroyd-B nanofluid along a stretching sheet is investigated. Recent studies have assumed that the nanoparticle fraction can be actively controlled on the boundary, similar to the temperature. However, in practice, such control presents significant challenges and in this study the nanoparticle flux at the boundary surface is assumed to be zero. We have used a relatively novel numerical scheme; the spectral relaxation method to solve the momentum, heat and mass transport equations. The accuracy of the solutions has been determined by benchmarking the results against the quasilinearisation method. We have conducted a parametric study to determine the influence of the fluid parameters on the heat and mass transfer coefficients.

Uncertainty quantification for the trailing-edge noise of a Controlled-Diffusion airfoil

Abstract: Two deterministic incompressible flow solvers are coupled with a nonintrusive stochastic collocation method to propagate several aerodynamic uncertainties of the same type encountered in a standard trailing-edge noise experiment of a low-speed controlled-diffusion airfoil to predict the far-field noise. Reynolds-averaged Navier–Stokes and large-eddy simulations are applied to a common restricted domain surrounding the airfoil embedded in the potential core of the jet in the anechoic wind-tunnel experiment. Both simulation methods provide the wall-pressure fluctuations near the airfoil trailing edge, which are then used in Amiet’s acoustic analogy for trailing-edge noise. In the Reynolds-averaged Navier–Stokes simulations, two different representative models are used to reconstruct the wall-pressure fluctuations: Rozenberg’s deterministic model directly based on integral boundary-layer parameters, and Panton and Linebarger’s statistical model based on the velocity field in the boundary layer. The nonintrus...

The effects of non-uniform flow velocity on vibrations of single-walled carbon nanotube conveying fluid

Abstract: The vibrational behavior of a viscous nanoflow-conveying single-walled carbon nanotube (SWCNT) was investigated The non-uniformity of the flow velocity distribution caused by the viscosity of fluid and the small-size effects on the flow field was considered Euler-Bernoulli beam model was used to investigate flow-induced vibration of the nanotube, while the non-uniformity of the flow velocity and the small-size effects of the flow field were formulated through Knudsen number (K n ), as a discriminant parameter For laminar flow in a circular nanotube, the momentum correction factor was developed as a function of K n For K n = 0 (continuum flow), the momentum correction factor was found to be 133, which decreases by the increase in K n may even reach near 1 for the transition flow regime We observed that for passage of viscous flow through a nanotube with the non-uniform flow velocity, the critical continuum flow velocity for divergence decreased considerably as opposed to those for the uniform flow velocity, while by increasing K n , the difference between the uniform and non-uniform flow models may be reduced In the solution part, the differential transformation method (DTM) was used to solve the governing differential equations of motion

Geometry effect of isolated roughness on boundary layer transition investigated by tomographic PIV

Abstract: Transitional flow over isolated roughness elements is investigated in the incompressible flow regime using Tomographic PIV. Three different geometries are considered (micro-ramp, cylinder and square) with same height and span. Their effect on accelerating boundary layer transition is compared and discussed. The measurement domain encompasses the full transition process and the flow development until the turbulent regime is established. The mean flow topology reveals a single pair of streamwise vortices for the micro-ramp as opposed to the additional pair associated to the horseshoe vortex around cylindrical and square elements. The statistical analysis of velocity fluctuations indicates a transition process induced from the point where the streamwise vortices induce an inflexional velocity profile. The cascade progresses downstream with a localized fluctuations increase at the turbulent-non-turbulent interface. The instantaneous flow topology contributes in explaining the transition mechanism, which appears to be dominated by hairpin-like vortices concentrating at the laminar-turbulent interface.

Minimal geodesics along volume preserving maps, through semi-discrete optimal transport

Abstract: We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L2 metric, which as observed by Arnold solve Euler's equations of inviscid incompressible fluids. The method relies on the generalized polar decomposition of Brenier, numerically implemented through semi-discrete optimal transport. It is robust enough to extract non-classical, multi-valued solutions of Euler's equations, for which the flow dimension is higher than the domain dimension, a striking and unavoidable consequence of this model. Our convergence results encompass this generalized model, and our numerical experiments illustrate it for the first time in two space dimensions.