The significance of drop-fluid viscosity on the effective rheological properties and on the dynamics of the microstructure of mono-disperse suspensions of two-dimensional liquid drops with constant interfacial tension is investigated by means of numerical simulations at vanishing Reynolds number, using the boundary integral method for Stokes flow. Three important features of the numerical method are the computation of the doubly-periodic Green's function and associated stress tensor by tabulation and interpolation, the iterative solution of a deflated integral equation for the interfacial velocity, and the repositioning of the drop interfaces at close proximity to avoid artificial coalescence. In the first part of the simulations, the interaction of two intercepting drops in simple shear flow is studied in an extended range of conditions, and the results are used to quantify the behaviour and develop insights into the physics of dilute systems. In the second part of the simulations, the motion of a random suspension of 25 drops repeated periodically in the two spatial directions is studied at the areal fraction ϕ=0.30, drop fluid to ambient fluid viscosity ratio λ=1 or 10, and drop capillary number Ca=0.10 or 0.30, a total of four combinations. It is found that the rheological properties of the suspension and the average drop deformation and orientation depend on the values of λ and Ca in a subtle fashion. As the viscosity of the drops is raised, the drop-centre pair distribution function undergoes a transition from a liquid-like to a rigid-particle-like behaviour, and particle aggregation and cluster formation become more important. For λ=10, the results are in excellent qualitative, and in some cases quantitative, agreement with those presented in previous studies for mono-layered suspensions of rigid spheres. The drop self-diffusivity is computed and its dependence on λ and Ca is discussed, although the results carry some uncertainty owing to the moderate number of drops within each periodic cell.
The shearing motion of monodisperse suspensions of two-dimensional deformable liquid drops with uniform interfacial tension is studied by means of numerical simulations. In the theoretical model, the drops are distributed randomly within a square that is repeated periodically in two directions yielding a doubly periodic flow. Under the assumption that inertial effects are negligible and the viscosity of the drops is equal to that of the suspending fluid, the motion is investigated as a function of the area fraction of the suspended drops and of the capillary number. The evolution of the suspension from an initial configuration with randomly distributed circular drops is computed using an improved implementation of the method of interfacial dynamics which is based on the standard boundary integral formulation for Stokes flow. The numerical procedure incorporates the method of multipole expansions to account for far-drop interactions, and interpolation through tables for computing the doubly periodic Green's function; the latter allows considerable savings in the cost of the computations. Dynamic simulations are carried out for suspensions with up to 49 drops within each periodic cell, for an extended period of time up to kt = 60, where k is the shear rate. Comparisons with previous numerical results for solid particles reveal that particle deformability and interfacial mobility play an important role in the character of the motion. The effects of particle area fraction and capillary number on the effective rheological properties of the suspension are discussed, and the statistics of the drop motion is analysed with reference to the drop-centre pair distribution function and probability density functions of drop aspect ratio and inclination. It is found that the effective rheo-logical properties may be predicted with remarkable accuracy from a knowledge of the instantaneous mean drop deformation and orientation alone, even at high area fractions. Cluster formation is not as important as in suspension of solid particles. The apparent random motion of the individual drops, when viewed at a sequence of time intervals that are large compared to the inverse shear rate, is described in terms of an effective non-isotropic long-time diffusivity tensor, and the transverse component of this tensor is computed from the results of the simulations with some uncertainty.
This paper describes the development and results of numerical models describing parachute inflation behavior. The models were developed using Fluid Structure Interaction (FSI) techniques in the commercially available transient dynamic finite element code LS-DYNA. Prior to 2009, FSI simulation methodologies developed at Airborne Systems had restricted analysis to the steady-descent phase of parachute operations. That is to say the modeling was performed in an infinite mass scenario, where the parachute does not influence the freestream air velocity; such models can be compared to tests conducted in a wind tunnel or during the steady descent phase of operation. Funding provided by NSRDEC in 2009/10 enabled Airborne Systems to develop a simulation methodology that is capable of assessing parachute performance in a finite mass scenario. Such a scenario enables the more complex inflation phase of a parachute to be investigated. In addition, the availability of experimental data, describing parachute inflation, has until recently proved limiting in quantifying the accuracy of simulation techniques. The availability of test data from a series of indoor vertical parachute tests conducted at the Space Power Facility at NASA Glenn Research Center Plum Brook Station provided an excellent means of code result validation. The experimental test setup produced a sufficiently controlled and instrumented environment specifically developed for basic parachute performance data collection. The results of the modeling, discussed herein, compare favorably with the indoor vertical parachute tests, with good prediction of both inflation force and post inflation breathing frequency. The models were developed prior to test data reduction and analysis, and as such acted as a true prediction. Nomenclature Cd = Drag coefficient D 0 = Nominal diameter PIA = Parachute Industries Association
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