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arXiv2014

Implicit Large Eddy Simulation of Cavitation in Micro Channel Flows

We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating multi-phase flows in fuel injectors and follows an experimental study of Iben et al., 2010. While a diesel-like test fuel was used in the experiment, we solve the compressible Navier-Stokes equations with a barotropic equation of state for water and vapor and a simple phase-change model based on equilibrium assumptions. Our LES resolve all wave dynamics in the compressible fluid and the turbulence production in shear layers.

physics.flu-dyn↗

arXiv2014

Collective behaviour of large number of vortices in the plane

We investigate the dynamics of $N$ point vortices in the plane, in the limit of large $N$. We consider {\em relative equilibria}, which are rigidly rotating lattice-like configurations of vortices. These configurations were observed in several recent experiments [Durkin and Fajans, Phys. Fluids (2000) 12, 289-293; Grzybowski {\em et.al} PRE (2001)64, 011603]. We show that these solutions and their stability are fully characterized via a related {\em aggregation model} which was recently investigated in the context of biological swarms [Fetecau {\em et.al.}, Nonlinearity (2011) 2681; Bertozzi {\em et.al.}, M3AS (2011)]. By utilizing this connection, we give explicit analytic formulae for many of the configurations that have been observed experimentally. These include configurations of vortices of equal strength; the $N+1$ configurations of $N$ vortices of equal strength and one vortex of much higher strength; and more generally, $N+K$ configurations. We also give examples of configurations that have not been studied experimentally, including $N+2$ configurations where $N$ vortices aggregate inside an ellipse. Finally, we introduce an artificial ``damping'' to the vortex dynamics, in an attempt to explain the phenomenon of crystalization that is often observed in real experiments. The diffusion breaks the conservative structure of vortex dynamics so that any initial conditions converge to the lattice-like relative equilibrium.

cond-mat.quant-gas↗

arXiv2014

Feedback control of inertial microfluidics using axial control forces

Inertial microfluidics is a promising tool for many lab-on-a-chip applications. Particles in channel flows with Reynolds numbers above one undergo cross-streamline migration to a discrete set of equilibrium positions in square and rectangular channel cross sections. This effect has been used extensively for particle sorting and the analysis of particle properties. Using the lattice Boltzmann method, we determine equilibrium positions in square and rectangular cross sections and classify their types of stability for different Reynolds numbers, particle sizes, and channel aspect ratios. Our findings thereby help to design microfluidic channels for particle sorting. Furthermore, we demonstrate how an axial control force, which slows down the particles, shifts the stable equilibrium position towards the channel center. Ultimately, the particles then stay on the centerline for forces exceeding a threshold value. This effect is sensitive to particle size and channel Reynolds number and therefore suggests an efficient method for particle separation. In combination with a hysteretic feedback scheme, we can even increase particle throughput.

physics.flu-dyn↗

arXiv2014

Centralised versus Decentralised Active Control of Boundary Layer Instabilities

We use linear control theory to construct an output feedback controller for the attenuation of small-amplitude Tollmien-Schlichting (TS) wavepackets in a flat-plate boundary layer.We distribute evenly in the spanwise direction up to 72 localized objects near the wall (18 disturbances sources, 18 actuators, 18 estimation sensors and 18 objective sensors). In a fully three-dimensional configuration,the interconnection between inputs and outputs becomes quickly unfeasible when the number of actuators and sensors increases in the spanswise direction. The objective of this work is to understand how an efficient controller may be designed by connecting only a subset of the actuators to sensors, thereby reducing the complexity of the controller, without comprising the efficiency. We find that using a semi-decentralized approach - where small control units consisting of 3 estimation sensors connected to 3 actuators are replicated 6 times along the spanwise direction - results only in a 11% reduction of control performance. Our results reveal that the best performance is obtained for a control unit which (i) is sufficiently wide to account for the full spanwise scale of the wavepacket when it reaches the actuators and (ii) is designed to account for the perturbations which are coming from the lateral sides (crosstalk) of the estimation sensors. We have also found that the influence of crosstalk is not as essential as the spreading effect.

physics.flu-dyn↗

arXiv2014

A family of energy stable, skew-symmetric finite difference schemes on collocated grids

A simple scheme for incompressible, constant density flows is presented, which avoids odd-even decoupling for the Laplacian on a collocated grids. Energy stability is implied by maintaining strict energy conservation. Momentum is conserved. Arbitrary order in space and time can easily be obtained. The conservation properties hold on transformed grids.

physics.flu-dyn↗

arXiv2014

Generalized squirming motion of a sphere

A number of swimming microorganisms such as ciliates ($\textit{Opalina}$) and multicellular colonies of flagellates ($\textit{Volvox}$) are approximately spherical in shape and swim using beating arrays of cilia or short flagella covering their surfaces. Their physical actuation on the fluid may be mathematically modeled as the generation of surface velocities on a continuous spherical surface -- a model known in the literature as squirming, which has been used to address various aspects of the biological physics of locomotion. Previous analyses of squirming assumed axisymmetric fluid motion and hence restricted all swimming kinematics to take place along a line. In this paper we generalize squirming to three spatial dimensions. We derive analytically the flow field surrounding a spherical squirmer with arbitrary surface motion, and use it to derive its three-dimensional translational and rotational swimming kinematics. We then use our results to physically interpret the flow field induced by the swimmer in terms of fundamental flow singularities up to terms decaying spatially as $\sim 1/r^3$. Our results will enable to develop new models in biological physics, in particular in the area of hydrodynamic interactions and collective locomotion.

physics.flu-dyn↗

arXiv2014

Liquid Metal Transformers

The room temperature liquid metal is quickly emerging as an important functional material in a variety of areas like chip cooling, 3D printing or printed electronics etc. With diverse capabilities in electrical, thermal and flowing behaviors, such fluid owns many intriguing properties that had never been anticipated before. Here, we show a group of unconventional phenomena occurring on the liquid metal objects. Through applying electrical field on the liquid metals immersed in water, a series of complex transformation behaviors such as self-assembling of a sheet of liquid metal film into a single sphere, quick mergences of separate metal droplets, controlled self-rotation and planar locomotion of liquid metal objects can be realized. Meanwhile, it was also found that two accompanying water vortexes were induced and reliably swirled near the rotating liquid metal sphere. Further, effects of the shape, size, voltage, orientation and geometries of the electrodes to control the liquid metal transformers were clarified. Such events are hard to achieve otherwise on rigid metal or conventional liquid spheres. This finding has both fundamental and practical significances which suggest a generalized way of making smart soft machine, collecting discrete metal fluids, as well as flexibly manipulating liquid metal objects including accompanying devices.

cond-mat.soft↗

arXiv2014

Electrokinetic instability in the sharp interface limit: The perpendicular electric field case

In this paper, instability at an interface between two miscible liquids with identical mechanical properties but different electrical conductivities is analyzed in the presence of an electric field that is perpendicular to the interface. A parallel electric field case was considered in a previous work [1]. A sharp Eulerian interface is considered between the two miscible liquids. Linear stability analysis leads to an analytic solution for the critical condition of instability. The mechanism of instability is analyzed. Key differences between the perpendicular and parallel electric field cases are discussed. The effect of a microchannel geometry is studied and the relevant non-dimensional parameters are identified.

physics.flu-dyn↗

arXiv2014

Fluctuating Immersed Material (FIMAT) Dynamics for Fully Resolved Simulation of the Brownian Motion of Particles

Fluctuating hydrodynamics based techniques have been developed in recent years for the simulation of Brownian motion of particles. These mesoscale simulation tools are viable approaches for problems where molecular dynamics simulations may be deemed expensive. We have developed a rigid constraint-based formulation where the key idea is to assume that the entire domain is a fluctuating fluid. Rigid motion constraints are then imposed in regions that are occupied by rigid particles. The resulting solution gives the Brownian motion of the particles. This approach is shown to be viable for the simulation of long time scale diffusive behavior as well as for short time scale dynamics by using two separate solution techniques. Test cases are reported to validate the approach and to establish its efficacy.

physics.flu-dyn↗

arXiv2014

Nonextensive statistical dynamics applied to wall turbulence

We apply a formalism of nonextensive statistical mechanics to experimental wall turbulence data, for the first time to our knowledge. Wind tunnel data for velocity differences a streamwise distance $r$ apart are compared to the prediction from theory as developed by Beck. The simplest theory, in which all free parameters are removed, is found to reproduce statistics for the wall-normal velocity component remarkably well, even for $r$ well beyond the corresponding integral scale, while the corresponding description of the streamwise velocity fluctuations is reasonable at separations below the integral scale. A least-squares 2-parameter fit is performed, and the dependence of the optimum parameter values on wall separation and $r$ is analysed. Both parameters are found to be approximately independent of wall-separation in the logarithmic sub-layer.

physics.flu-dyn↗

arXiv2014

Controlling inertial focussing using rotational motion

In inertial microfluidics lift forces cause a particle to migrate across streamlines to specific positions in the cross section of a microchannel. We control the rotational motion of a particle and demonstrate that this allows to manipulate the lift-force profile and thereby the particle's equilibrium positions. We perform two-dimensional simulation studies using the method of multi-particle collision dynamics. Particles with unconstrained rotational motion occupy stable equilibrium positions in both halfs of the channel while the center is unstable. When an external torque is applied to the particle, two equilibrium positions annihilate by passing a saddle-node bifurcation and only one stable fixpoint remains so that all particles move to one side of the channel. In contrast, non-rotating particles accumulate in the center and are pushed into one half of the channel when the angular velocity is fixed to a non-zero value.

physics.flu-dyn↗

arXiv2014

A meshless method for compressible flows with the HLLC Riemann solver

The HLLC Riemann solver, which resolves both the shock waves and contact discontinuities, is popular to the computational fluid dynamics community studying compressible flow problems with mesh methods. Although it was reported to be used in meshless methods, the crucial information and procedure to realise this scheme within the framework of meshless methods were not clarified fully. Moreover, the capability of the meshless HLLC solver to deal with compressible liquid flows is not completely clear yet as very few related studies have been reported. Therefore, a comprehensive investigation of a dimensional non-split HLLC Riemann solver for the least-square meshless method is carried out in this study. The stiffened gas equation of state is adopted to capacitate the proposed method to deal with single-phase gases and/or liquids effectively, whilst direct applying the perfect gas equation of state for compressible liquid flows might encounter great difficulties in correlating the state variables. The spatial derivatives of the Euler equations are computed by a least-square approximation and the flux terms are calculated by the HLLC scheme in a dimensional non-split pattern. Simulations of gas and liquid shock tubes, moving shock passing a cylinder, internal supersonic flows in channels and external transonic flows over aerofoils are accomplished. The current approach is verified by extensive comparisons of the produced numerical outcomes with various available data such as the exact solutions, finite volume mesh method results, experimental measurements or other reference results.

physics.flu-dyn↗

arXiv2014

DNS and LES of two-phase flows with cavitation

We report on recent progress in the physical and numerical modeling of compressible two-phase flows that involve phase transition between the liquid and gaseous state of the fluid. The high-speed dynamics of cavitation bubbles is studied in well-resolved simulations (DNS) with a sharp-interface numerical model on a micro scale. The underlying assumption of the employed evaporation/condensation model is that phase change occurs in thermal non-equilibrium and that the associated timescale is larger than that of the wave dynamics. Results for the collapse of a spherical vapor bubble close to a solid wall are discussed for three different bubble-wall configurations. The major challenge for such numerical investigations is to accurately reproduce the dynamics of the interface between liquid and vapor during the entire collapse process, including the high-speed dynamics of the late stages, where compressibility of both phases plays a decisive role. Direct interface resolving simulations are intractable for real world technical applications such as turbulent flows involving cavitation clouds with millions of vapor bubbles and a wide range of time and length scales. For this reason, we developed a coarse grained model for large-eddy simulation (LES) of turbulent two-phase flows with cavitation. In LES, vapor bubbles constitute sub-grid scales that have to be modeled accordingly. On the grid scale, we solve the compressible Navier-Stokes equations for a homogeneous mixture of liquid and vapor. For deriving an appropriate equation of state, we assume that the characteristic time scale of phase change is much smaller than the numerical time step and that phase change is isentropic and in mechanical equilibrium at the saturation pressure. This macroscopic model is applied to realistic technical problems and to more generic flows to study the mutual interaction of turbulence and cavitation.

physics.flu-dyn↗

arXiv2014

Free surface flow due to a submerged source

In this thesis we consider the free surface flow due to a submerged source in a channel of finite depth. This problem has been considered previously in the literature, with some disagreement about whether or not a train of waves exist on the free surface for Froude numbers less than unity. The physical assumptions behind the accepted model are clearly stated and governing equations and boundary conditions derived. Complex variable theory is then employed to obtain a singular nonlinear integral equation, which describes the flow field completely. The integral equation is evaluated numerically using a collocation method, and implemented with mathematical software {\em Matlab}. The numerical solutions suggest that indeed waves do exist on the free surface, but are exponentially small in the limit that the Froude number approaches zero. An asymptotic expression is also derived to solve the integral equation, valid for small Froude numbers. This expansion is calculated to second order, which improves on the leading order solution given previously in the literature. Such a scheme is unable to predict waves on the free surface, since they are exponentially small. It is discussed how exponential asymptotics could be used to derive a more accurate analytic solution that describes waves on the free surface.

physics.flu-dyn↗

arXiv2014

Exact coherent structures in a reduced model of parallel shear flow

A reduced description of shear flows consistent with the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow [J. Wang et al., Phys. Rev. Lett. 98, 204501 (2007)] is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for Waleffe flow [F. Waleffe, Phys. Fluids 9, 883--900 (1997)]. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced model provides a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows.

physics.flu-dyn↗

arXiv2014

Investigation of acoustic streaming patterns around oscillating sharp edges

Oscillating sharp edges have been employed to achieve rapid and homogeneous mixing in microchannels using acoustic streaming. Here we use a perturbation approach to study the flow around oscillating sharp edges in a microchannel. This work extends prior experimental studies to numerically characterize the effect of various parameters on the acoustically induced flow. Our numerical results match well with the experimental results. We investigated multiple device parameters such as the tip angle, oscillation amplitude, and channel dimensions. Our results indicate that, due to the inherent nonlinearity of acoustic streaming, the channel dimensions could significantly impact the flow patterns and device performance.

physics.flu-dyn↗

arXiv2014

Computations of Nonlinear Propagation of Sound Emitted from High Speed Mixing Layers

Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of convective Mach numbers of 0.4, 0.8 and 1.2. The LES results agree qualitatively with known flow behavior. Mach waves are observed in the near sound field of the supersonic mixing layer computed by the LES. These waves show steepening typical to non-linear propagation. Further calculations using the Burgers equation support this finding, where the initial wave slope has a role in kicking them. No visible non-linear propagation effects were found for the subsonic mixing layers. The effects of geometrical spreading and viscosity are also considered.

physics.flu-dyn↗

arXiv2014

Numerical Study on Mechanism of Multiple Rings Formation

In this paper, the flow around each ring-like vortex is investigated by high order DNS including first sweep, first ejection, second sweep, second ejection, positive spike, momentum deficit, vortex shape, vortex location, strength of sweeps, etc. Meanwhile, the mechanism about formation of momentum deficit is deeply studied. A new mechanism on how the multiple rings are formed one by one found both by experiment and by DNS in late boundary layer transition is presented. It also reveals that the relation between streamwise vortex and spanvise vertex rings, and how the vorticity is transferred between them.

physics.flu-dyn↗