Nonlinear axisymmetric shape oscillations of an inviscid liquid drop in a vacuum are investigated theoretically for their relevance for transport processes across the drop surface. The weakly ...nonlinear approach is adopted as the theoretical method. For the two-lobed mode of deformation $m=2$, known nonlinear effects are an asymmetry of the times the drop spends in the oblate and prolate deformed states, and an oscillation frequency smaller than the linear one found by Rayleigh. The present analysis shows that, for $m=2$, the frequency decrease with increasing surface deformation of the droplet is a third-order effect. For higher deformation modes, the frequency decrease shows in the second-order approximation already. The analysis is carried out for modes of initial deformation up to $m=4$, but not limited to that. The nonlinearity is due to two different contributions: the coupling of different modes of deformation; and the forces from capillary pressure acting on different drop cross-sectional areas in different phases of the oscillation. For the two-lobed mode of deformation, at an aspect ratio of 1.5, the two effects reduce the oscillation frequency by 5 %. The present analysis represents the quasi-periodicity of nonlinear drop oscillations found by other authors in numerical simulations. The results show that drops in nonlinear oscillations at strong deformation may never reach the spherical shape, thus exhibiting a resultant increase of their surface area.
Sprays produced by pressure atomization of various liquids are investigated experimentally, showing the self-similar flow fields of both the liquid and the gas phases. Phase-Doppler measurements are ...conducted in the sprays at varying radial and axial distances from the atomizer orifice. The theoretical description of the gas flow field based on boundary-layer theory reveals a self-similar velocity field driven by momentum transfer from the liquid phase ejected into the gaseous environment. The momentum loss of the liquid droplet phase is also found to be self-similar, which was to be expected, but not shown in the literature before. The analytical self-similar description of the two-phase flow field is in excellent agreement with the experimental data.
A universal modelling approach of drop fragmentation after head-on drop collisions is presented. In this approach, the colliding drops are seen as liquid springs that coalesce, compress and relax, ...leading the merged drop to break up if it reaches a critical aspect ratio. Combining energetic balance of the compression and relaxation phases with a Rayleigh-like criterion, we deduce the fragmentation threshold velocity for the collision of two and three drops of the same liquid and of two drops of immiscible liquids. Predictions and experimental results obtained for these three kinds of collisions using various liquids and drop sizes are found to be in good agreement over a wide domain whose boundaries are discussed.
► Viscous liquid flow through a pressure-swirl atomizer was modelled and computed. ► At given pressure difference, higher liquid viscosity results in higher flow rate. ► Liquid film thickening at the ...orifice is the dominant reason for this phenomenon. ► Mass flow rates computed and measured agree very well. ► Air core radii computed agree very well with results from other sources.
We study theoretically the viscous flow through the swirl chamber of a pressure-swirl atomizer. The aim is to predict quantitatively the flow rate of a given liquid driven by a given pressure difference across the atomizer in order to explain the counter-intuitive experimental finding that, for moderate liquid dynamic viscosities, at a given driving pressure difference and atomizer geometry, a higher liquid viscosity results in a higher flow rate. The concept for the flow analysis is to subdivide the flow field in the swirl chamber into zones allowing for neglect of velocity components or boundary-layer simplification. The result is a quantitative prediction of the liquid flow rate for a given driving pressure difference and atomizer geometry, and for given liquid properties relevant for the discharge from the atomizer. Flow rates are compared to experimental data from various sources and show good agreement. Another part of the results is the diameter of the air core formed around the symmetry axis of the swirl chamber, which is of sub-millimetric order here. This result is compared to different experimental correlations and also shows very good agreement. For small values of the swirl velocity and/or very high liquid viscosities, the air core breaks down. The phenomenon of air core break down has been analysed, and it is shown that for high viscosities the air core breaks down due to weak swirl velocity.
•Polymer solution deformation retardation time is measured with oscillating drops.•Individual drops are levitated acoustically and perform damped shape oscillations.•Deformation retardation times of ...polyacrylamide solutions are around 100μs±15%.•The deformation retardation time depends weakly on uncertainties of input quantities.
The use of the oscillating drop method for measuring the deformation retardation time λ2 of viscoelastic liquids is proposed. For small oscillation amplitudes, λ2 may be determined from the characteristic equation of the drop derived from linear theory. In the experiment an acoustically levitated individual drop is excited to shape oscillations of the fundamental mode m=2 by ultrasound modulation. Once the excitation is terminated, the drop performs damped oscillations, and the angular frequency and damping rate are measured from drop shapes recorded by a high-speed camera. A numerical method is used for determining a pair of liquid properties from the characteristic equation – the liquid zero-shear dynamic viscosity η0 and the deformation retardation time λ2. The spherical Bessel functions involved in the equation produce a manifold of solutions, from which the correct one must be identified. Comparison of the computed value of η0 with the result from a rheometric liquid characterisation is found to be the right criterion for the identification. The values of λ2 obtained by this measurement are found to depend weakly on uncertainties of the experiment. They deviate strongly from the values typically used in simulations of viscoelastic liquid flow.
Computational modelling of a centrifugal technique for separating binary mixtures of thermoplastic polymers in the molten state is presented. The technique may be useful for the recycling of ...polymeric materials. The study investigates the physical process of component separation due to the centrifugal force in a batch process, showing the potential of using a dispersed model for describing the complex mechanism underlying the technique. Given the long time scales of change of the flow field, the polymer melts are modelled as inelastic, shear-thinning materials. The centrifugal force drives the component with the higher density to the outer region of an annular cross section occupied by the melt inside a rotating containment. The model system PET/LDPE is investigated in detail. The simulations allow to predict the process time needed for the separation. The simulations are the basis for studying a continuous process in a rotating tube.
A theoretical model for the evaporation of multi-component liquid droplets based on the model by Abramzon and Sirignano is presented and applied to the evaporation of acoustically levitated droplets. ...The liquid phase is treated as a thermodynamically real fluid, using the UNIFAC method for calculating the component activities, and the gas phase as ideal. Computational results, which consist in the droplet surface and volume, temperature and composition as functions of time, are verified by experiments carried out with single droplets evaporating in an acoustic levitator. The results are in excellent agreement, suggesting that the model correctly captures the physico-chemical phenomena in multi-component liquid droplet evaporation.
Binary collisions of drops of immiscible liquids are investigated experimentally at well-defined conditions of impact. In the experiments we vary all relevant properties of an aqueous and an oil ...phase, the impact parameter, the drop size and the relative velocity. The drops observed after the collisions exhibit three main phenomena: full encapsulation, head-on fragmentation, and off-centre fragmentation. The regimes characterized by these phenomena replace the ones observed in binary collisions of drops of the same liquid: coalescence, reflexive separation, and stretching separation. Our aim is a universal description of the two fragmentation thresholds of such collisions. Based on the capillary instability and an energy balance, we establish for head-on collisions a scaling law for the evolution of the threshold impact velocity with the properties of the liquids and the droplet size. The fragmentation threshold for off-centre collisions is compared to established models from the literature, which appear unsatisfactory. Introducing an effective impact parameter, which accounts empirically for the deformation and rotation of the drops upon impact, we describe this fragmentation threshold in a universal way. For both fragmentation thresholds, the agreement between experimental data and their theoretical representation is very good. Our work yields new insight into binary collisions of drops and proposes a perspective to develop a more general description with implications for binary collisions of drops of a single liquid as well.
Non-symmetric bi-stable flow around the Ahmed body Meile, W.; Ladinek, T.; Brenn, G. ...
The International journal of heat and fluid flow,
February 2016, 2016-02-00, 20160201, Letnik:
57
Journal Article
Recenzirano
•The non-symmetric bi-stable flow around the Ahmed body is investigated experimentally.•Bi-stability, described for symmetric flow by Cadot and co-workers, was found in nonsymmetric flow also.•The ...flow field randomly switches between two states.•The flow is subject to a spanwise instability identified by Cadot and co-workers for symmetric flow.•Aerodynamic forces fluctuate strongly due to the bi-stability.
The flow around the Ahmed body at varying Reynolds numbers under yawing conditions is investigated experimentally. The body geometry belongs to a regime subject to spanwise flow instability identified in symmetric flow by Cadot and co-workers (Grandemange et al., 2013b). Our experiments cover the two slant angles 25° and 35° and Reynolds numbers up to 2.784 × 106. Special emphasis lies on the aerodynamics under side wind influence. For the 35° slant angle, forces and moments change significantly with the yawing angle in the range 10° ≤ |β| ≤ 15°. The lift and the pitching moment exhibit strong fluctuations due to bi-stable flow around a critical angle β of ±12.5°, where the pitching moment changes sign. Time series of the forces and moments are studied and explained by PIV measurements in the flow field near the rear of the body.
An analytical solution of the problem of diffusional mass transport inside a spherical binary mixture droplet is presented. The droplet evaporates according to the
d
2-law. Mass fraction profiles of ...the mixture components are obtained as series expansions in confluent hypergeometric, Legendre and sine/cosine functions. The analytical description is valid for arbitrary ratio of the rate of shrinkage of the sphere surface to the diffusion coefficient in the liquid phase. The results allow for a prediction of the morphology of the dried particles, i.e., whether hollow or solid spheres result from the drying process. The field of application of the results presented is spray drying of solutions of solid substances.
