Drag Coefficient Of Droplet Research Articles

Effects of surface wettability on the aerodynamics of wind-driven droplets at the verge of shedding

An experimental study was conducted to investigate the time-averaged aerodynamics of sessile droplets at the verge of shedding on hydrophilic and hydrophobic surfaces. A high-resolution particle image velocimetry system was used to measure/reconstruct the velocity and pressure fields in the droplet symmetry plane and obtain the time-averaged aerodynamic loading. It was found that the stagnation angle (the angle bounded by the substrate and the ray emanating from the droplet center connecting to the stagnation point) decreases with decreasing contact angle due to the shrinking size of the horseshoe vortex. The air pressure reaches the maximum near the stagnation point and its minimum near the droplet apex where flow separation occurs. In the near wake of droplets, a recirculation region, where the velocity reduces to nearly zero and the pressure is low, is generated due to the flow separation. The normalized length of the recirculation region decreases with increasing contact angle since droplets with higher contact angles need flows with lower Reynolds number to reach the point of shedding. In addition, the aerodynamic drag over droplets was evaluated by the wake integral method, analyzing the contribution of momentum deficit, Reynolds stress, and pressure deficit. The drag coefficient of the droplets, at the verge of shedding, was independent of the contact angle. This work shows that the drag coefficient of droplets with different contact angles at the verge of shedding can be similar even though the droplet shape, Reynolds number, and flow structures are different.

Scaling formulation of multiphase flow and droplet trajectories with rime ice accretion on a rotating wind turbine blade

In this paper, scaling and similitude are investigated for ice accretion on a rotating wind turbine blade. Numerical CFD icing simulations are performed using FENSAP ICE software to test the scaling methods and verify the results. A small blade section is scaled six times, and each case is tested at specific flow conditions. Scaled conditions for velocity (streamwise and rotational), droplet size, and icing time are examined. CFD solutions for the flow field (air and droplet) are obtained in terms of the velocity, droplet trajectories, pressure coefficient distributions, ice thickness, and ice shapes, by quantifying the significant parameters involved in the icing process. Recommendations for parameters to be used for rime ice scaling on a rotating blade are presented, and numerical results are reported to support those recommendations. Numerical results and test conditions are obtained at sea level in wind tunnel facilities for experimental investigation. This paper presents the formulation of non-dimensionlized governing equations for scaling of the flow field, droplet trajectories, and ice accretion on a rotating blade model. It derives a set of non-dimensional groups which govern the flow parameters for a rotating blade, including the Strouhal number, Froude number, drag coefficient of droplets and droplet based Reynolds number, droplet inertia parameter, and two other new parameters. The scaling methodology can also be utilized to determine alternative test conditions to predict rime ice conditions on a rotating blade. The study provides valuable insight to predict ice accretion on large wind turbine blade sections in the field based on scaled smaller blade sections tested in a laboratory setting.

Application of multiphase flow and droplet separation theory in modeling cough droplets contamination range to mitigate COVID-19 transmission: Do not stand too close to me!

On March 11, 2020, the World Health Organization (WHO) declared that COVID-19 is a pandemic, warning the world of a health catastrophe and social, economic, and political disruptions. According to WHO, COVID-19 is transmitted by the transport of respiratory droplets generated by a violent respiratory event such as sneeze and cough directly to susceptible persons, or indirectly through surfaces. The aim of this study is to propose simple physical and mathematical models based on two-phase flow dynamics and droplet separation theory. The proposed mathematical model predicts the contamination range of ejected cough droplets, estimating the safe person-to-person social distance. As a result, the proposed simple model predicted a contamination range of 2.3 m for a male adult. In addition, to understand the behavior of ejected cough droplets, a sensitivity analysis is carried out to investigate the effect on contamination range of cough air flowrate, i.e., body/lung size, droplet size, and droplet drag coefficient. It is found that as the body/lung size decreases, i.e., lower cough flow rate, contamination range decreases, resulting in 1.9 m for an adult female, and 1.4 m for a child. In addition, the model predictions show an appreciable effect of droplet size, and droplet drag coefficient on cough contamination range. In particular, the effect of droplet drag coefficient is of interest, because of its relationship to ambient conditions such as temperature and relative humidity, in which both affect ambient air viscosity, and thus drag coefficient. This is important in investigating the contamination range and person-to-person social-distance as climate changes.

A Numerical Investigation on Droplet Bag Breakup Behavior of Polymer Solution.

The deformation and breakup of a polymer solution droplet plays a key role in inkjet printing technology, tablet-coating process, and other spray processes. In this study, the bag breakup behavior of the polymer droplet is investigated numerically. The simple coupled level set and volume of fluid (S-CLSVOF) method and the adaptive mesh refinement (AMR) technique are employed in the droplet breakup cases at different Weber numbers and Ohnesorge numbers. The nature of the polymer solution is handled using Herschel–Bulkley constitutive equations to describe the shear-thinning behavior. Breakup processes, external flow fields, deformation characteristics, energy evolutions, and drag coefficients are analyzed in detail. For the bag breakup of polymer droplets, the liquid bag will form an obvious reticular structure, which is very different from the breakup of a Newtonian fluid. It is found that when the aerodynamic force is dominant, the increase of the droplet viscous force will prolong the breakup time, but has little effect on the final kinetic energy of the droplet. Moreover, considering the large deformation of the droplet in the gas flow, a new formula with the cross-diameter (Dcro) is introduced to modify the droplet drag coefficient.

Motion of Nanofluid Droplets through Immiscible Quiescent Liquid: An Experimental Study

Motion of droplets in liquid –liquid extraction column is of importance for many industrial processes. This study aims at evaluation of hydrodynamic behavior of a nanofluid particle moving through an immiscible liquid. Toluene based nanofluids were used as referral systems in this study. Nanoparticles of ZnO, Al2O3, SiO2 and TiO2 have been used to synthesize stable nanofluids. The experiments were carried out using different concentrations of nanoparticles to study the variation in terminal velocity, drag coefficient and eccentricity of the nanofluid droplet. Observations show enhancement in terminal velocity and reduction in drag coefficient of the droplets, for all nanofluids up to optimum concentration of nanoparticles. With increase in concentration of nanofluid beyond the optimum concentration, the droplet terminal velocity decreases and drag coefficient increases due to deformation in shape and an increase in oscillation that could be due to nanoparticle aggregation in nanofluid. The eccentricity of...

On the transient flow inside and around a deforming millimetre class oil droplet falling under the action of gravity in stagnant air

The liquid flow inside, and the induced air flow around, a falling droplet in stagnant air was numerically investigated using the volume of fluid method to describe the droplet interface. The droplet consisted of oil with the same surface tension and with viscosity as parameter. It was injected into stagnant air with an initial velocity of 1 m/s; therefore, the initial Weber (We = 0.14), Reynolds (Re = 141), and Bond (Bo = 2.4) numbers remained constant during the parametric study whilst the initial Capillary (Ca) and Ohnesorge (Oh) numbers varied by an order of magnitude from 0.46 to 4.6 and from 0.044 to 0.44, respectively. We examined the effect of viscosity on the flow inside, and around, the droplet as well as on the droplet deformation and its natural frequency. This investigation showed a strong dependence of the deformation with liquid viscosity. Specifically, the droplets achieved their final deformation in under-damped, for low viscosity, and in over-damped, for high viscosity, oscillation modes. After a critical time tcrit (or Recrit), the instantaneous air flow symmetry was disturbed, initially in the wake and soon after in the interior of the droplet and in the vortex shedding downstream of the droplet. The air flow in the wake region detached from the droplet surface and resulted in a wake which was approximately 1.5 times longer and wider than the wake behind a solid sphere at the same Re number at steady state conditions. A roller-vortex structure (called rollex) was established upon injection in the immediate wake of the droplet, forming the necessary kinematic link between the directions of the internal circulation in the droplet (Hill vortex) and of the external recirculating air flow in the droplet’s wake. The droplet drag coefficients were compared with corresponding values used in droplet breakup models: although, ultimately, the droplet drag coefficient converged to the values given by the models, the initial magnitudes after injection were incorrect.

Drag Coefficient of a Spherical Droplet Immersed in a Near-Critical Binary Fluid Mixture

We consider a spherical liquid droplet immersed in a near-critical binary fluid mixture. A weak preferential attraction is assumed between the droplet and one of the two mixture components, and the difference in the viscosity is neglected between the mixture components. Using the Gaussian free-energy functional, we calculate the drag coefficient of a droplet. Whether it is increased or decreased by the preferential attraction turns out to depend on the bulk correlation length and the ratio of the viscosity of the surrounding mixture to that of the droplet.

Finite-volume droplet trajectories for icing simulation

During a Lagrangian icing simulation a large number of droplet trajectories are calculated to determine the water catch, and as a result it is important that this procedure is as rapid as possible. In order to arrive at a method with minimum complexity, a finite-volume representation is developed for streamlines and extended to incorporate the equations of motion for a droplet, with all cells being crossed in a single timestep. However, since cells vary greatly in size, the method must be implicit to avoid an awkward stability restriction that would otherwise degrade performance. An implicit method is therefore implemented by carrying out iterations to solve for the crossing of each CFD cell, so that the droplet motion is tightly coupled to the underlying flow and mesh. By crossing every cell in a single step, and by using the mesh connectivity to track the droplet motion between cells, any need for costly searches or containment checks is eliminated and the resulting method is efficient. The implicit system is solved using functional iteration, which is feasible for the droplet system (which can be stiff) by using a particular factorisation. Stability of this iteration is explored and seen to depend primarily on the maximum power used in the empirical relationship for droplet drag coefficient CD=CD(Re), while numerical tests confirm the theoretical orders of accuracy for the different discretisations. Final results are validated against experimental and alternative numerical water catch data for a NACA 23012 aerofoil.

Modeling of flow field and separation efficiency of a deoiling hydrocyclone using large eddy simulation

In order to evaluate the separation efficiency and flow field of deoiling hydrocyclones a three dimensional simulation is performed using large eddy simulation (LES) approach. Although this approach has been used in other types of hydrocyclones, the present work is a primer application of the LES approach for simulation of deoiling hydrocyclones. Due to anisotropic behavior of flow inside the hydrocyclones, LES is a suitable method to predict the flow field since it resolves large scales and models isotropic small scales. Obtained velocity field using the LES approach in comparison with other turbulence models is in good agreement with available experimental velocity measurements. The method of Lagrangian particle tracking with an optimized search algorithm (closest cell) is also used to evaluate the separation efficiency of deoiling hydrocyclones. Special attention is drawn to droplet drag coefficient, while the differences between separation efficiency curves using modified drag coefficient are also highlighted.

Dynamics of a deformable, transversely rotating droplet released into a uniform flow

AbstractThe effects of transverse rotation on the dynamics of a droplet released into a uniform free stream are numerically investigated. The range of the dimensionless rotation rate is limited to $0\leq {\Omega }^{\ensuremath{\ast} } \leq 1$, to avoid any possibility of the droplet breaking up. Droplet dynamics and deformations undergo distinct changes when the dimensionless rotational rate $({\Omega }^{\ensuremath{\ast} } )$ reaches a critical value. The critical rotational rate ${{\Omega }_{crit} }^{\ensuremath{\ast} } $ is sensitive to the change in the density ratio, but less dependent on the viscosity ratio and interfacial tension. Below ${{\Omega }_{crit} }^{\ensuremath{\ast} } $, the droplet drag coefficients are reduced marginally as the effect of the rotation is quickly suppressed by the free stream. Above ${{\Omega }_{crit} }^{\ensuremath{\ast} } $, the drag coefficients decrease initially as the rotation effect dominates at earlier times, resulting in a global minimum. The drag coefficients increase monotonically at later times, when the rotation effects decrease and the free-stream effects become dominant. The only exception is with the increase in the viscosity ratio and the surface tension, which either inhibits droplet deformation or restores the droplet to a more spherical shape in the late stages of droplet evolution. The droplet also experiences lift due to the effects of the transverse rotation. It is observed that the lift coefficients are less dependent on the droplet frontal area as the lift is generated by the velocity difference between the upper and lower interface. In general, the lift coefficients increase with ${\Omega }^{\ensuremath{\ast} } $ at earlier times and decrease at later times as the difference in the velocity between the upper and lower interface decreases. In some extreme cases, the lift coefficients even become negative.

Model of droplet dynamics and evaporation for sprinkler irrigation

Information on droplet dynamics and evaporation from sprinklers is important for the design of irrigation systems. To obtain improved predictions, a modified mathematical model of droplet ballistics and evaporation for sprinkler irrigation was developed. Air drag force is an important factor affecting the droplet dynamics and evaporation. Five different schemes for calculating the air drag coefficient of droplet were compared and the optimal one was selected. From sensitivity analyses, it was concluded that droplet evaporation rate was most sensitive to droplet diameter for droplets 2 mm. The calculation scheme used by Park et al. {Transactions of the ASAE, 25(2), 357–361 (1982) and (3), 795–804, (1983)} was selected since it provided the best prediction of droplet flight distance. The model was verified using experimental results from droplet fall velocities and loss rates. The average relative error between the predicted and measured data of fall velocities and loss rates were 1.2% and 4.3%, respectively. The average relative error of the total evaporation rate between the predicted and measured data was 17.5%.

Choice of urea-spray models in CFD simulations of urea-SCR systems

The sensitivity of modeling choices to obtained results for Eulerian–Lagrangian CFD simulations of urea-SCR systems has been investigated for a system consisting of an AdBlue-spray located at the exhaust pipe wall, directed into the exhaust gas flow. The decomposition of urea is modeled as being heat transfer limited and taking place at a constant temperature (425 K). It is shown that modeling choices may affect the predicted extent of wall hit, which types of droplets that are predicted to hit the wall, and also where they will do so. The influence of the different forces due to drag, buoyancy, lift effects, thermophoresis and history effects was investigated, proving that only the forces due to drag and buoyancy are necessary to correctly describe droplet motion within this system. It is necessary to use a droplet drag coefficient that takes the current level of droplet distortion into account. A stochastic particle tracking model will describe the effects of turbulent dispersion, but also make the simulation results sensitive to the quality of the turbulence model's prediction of the turbulent fluctuating velocities. Using such a model will also resolve some of the enhancement of heat and mass transfer caused by the continuous acceleration/deceleration of droplets by turbulent eddies.

Vapor/liquid phase interaction in flare flashing sprays used in dermatologic cooling

Little knowledge exists concerning the atomization mechanisms and dispersion of flashing sprays in dermatologic cooling. This study examines flashing of a high superheat fluid flowing through micro tube nozzles resembling current medical devices. A one-dimensional, semi-empirical model of refrigerant flow through capillary tubes is used to quantify internal flow characteristics. These results provide nozzle exit conditions that are then correlated to external spray characteristics determined experimentally. One-dimensional expressions for external vapor/liquid interaction are developed to determine evolution of droplet size distribution and explain measured droplet accelerations near the nozzle exit. Droplet drag coefficients are subsequently calculated and compared to existing literature.

Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 μm and on the order of 1012 particles/m3, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.

Coalescence of Droplets of an Ink Jet. 2nd Report, Valuation of Drag Coefficient of Droplets by 2-D Cylinder Model.

In Hertz type ink jet printers, a liquid jet ejected from a 10 μm capillary tube into air breaks up to droplets, and after, some of the droplets are charged and the remaining non-charged droplets are used as dots for printing. We reported experimental results on the coalescence of droplets in a previous paper. In this paper, the flow patterns around two cylinders were analyzed in order to examine the drag of droplets by using a 2-D model. Experiments were carried out to visualize the flow past two circular cylinders arranged in a series in a water tunnel. The analytical results of the streamline agree with that of the experimental results qualitatively. The error of analysis and experiments of reduction ratio of drag coefficient between the first and second cylinders is 3.7% in the case of the first coalescence.

One‐dimensional numerical model for a spray column heat exchanger

AbstractA numerical model describing performance of a liquid‐liquid spray column heat exchanger is developed. The model is for a disperse packed column operating in steady state. The fundamental equations for the continuous and distributed phases are developed in Eulerian and Lagrangian forms, respectively. The model predicts simultaneously the volume fraction, velocity, and temperature for each phase. Energy and momentum are exchanged between phases through source variables. Empiricism in the model is limited to the specification of droplet drag coefficient and Nusselt number correlations which are utilized to calculate momentum and energy source terms. Application of the computer model to column operation yields predictions that compare closely with experimental results.

Numerical modeling of a vaporizing multicomponent droplet

A numerical investigation of the fundamental processes governing the energy, mass and momentum exchange between the liquid and gas phases of vaporizing, multicomponent liquid droplets is presented. The configuration studied is unsteady, axisymmetric and consists of an isolated, multicomponent droplet vaporizing in a high-temperature, convective, oxidative environment. the model considers the different volatilities of the liquid components, and accounts for variable liquid properties due to variation of the species concentrations as well as for non-Fickian multicomponent gaseous diffusion. Additional features include variable thermophysical properties in the gas phase, variable liquid viscosity, conductivity and heat of vaporization, consideration of the surface blowing effect and droplet surface regression due to vaporization, internal liquid circulation with transient droplet heating, and droplet deceleration with respect to the free flow due to drag. The numerical calculation employs finitedifference techniques and an iterative solution procedure. The time-varying spatially-resolved data for a bi-component (n-octane/benzene) liquid droplet show depletion of the more volatile liquid substance on the droplet surface due to preferential vaporization. The surface depletion is subsequently transferred to the droplet interior through convective mechanisms that develop as a result of the liquid-surface motion under the influence of the fast-moving surrounding gas. The preferential vaporization results in a gradual reduction of the more volatile species concentrations throughout the droplet interior with maximum concentrations occuring at regions around the center of the vortex formed within the droplet. An examination of the potential for microexplosion of the n-octane/benzene droplet, indicated no possibility of a catastrophic fragmentation under the conditions investigated. The bi-component droplet model was employed to examine the commonly used assumptions of unity Lewis number in the liquid phase and Fickian gaseous diffusion. We found that even though the individual surface quantities involved may change substantially, the droplet drag coefficients, the vaporization rates and the related transfer numbers are not influenced by the above assumptions in a significant way.

Interaction between two vaporizing droplets in an intermediate Reynolds number flow

The dynamic properties of two vaporizing droplets moving in tandem and interacting through hydrodynamic forces are presented for the intermediate Reynolds number range of droplet motion [Re=O(100)]. The problem is relevant for dense spray applications. Depending upon certain initial parameters, the droplets can collide or separate. The behaviors of the droplets are influenced by the mass and heat transport associated with the evaporation of droplets in air. Droplet-drag coefficient, Nusselt number, droplet mass, droplet Reynolds number, and droplet spacing histories are reported for a limited number of cases following the introduction of two droplets of different radii, a′1,0 and a′2,0, at a given initial spacing, a′0, into a hot, convective fluid, which is characterized by uniform free-stream conditions. A finite-difference solution of the coupled two-phase, unsteady Navier–Stokes equations in cylindrical coordinates on a body-fitted coordinate system is adjusted continually to accommodate the changing boundary shapes resulting from the droplet movement and evaporation. The interactions are significant for initial Reynolds number range of 50 to 200 and for initial droplet spacings of 2 to 15 droplet diameters. Drag coefficients and Nusselt numbers can differ significantly from the values for isolated droplets. Droplet collision is likely for the initially equal-sized droplets. Droplets moving in tandem collide for larger values of the ratio of the aft initial droplet diameter to the lead initial droplet diameter. A bifurcation value of this parameter is found above which increased separation of the droplets occurs. The bifurcation value increases as initial droplet spacing increases. This value depends only very weakly on the initial Reynolds number. For spacings above two diameters, the lead droplet behaves like an isolated droplet while drag coefficients for the aft droplet are significantly lower. Vaporization rate significantly affects the drag coefficients. For droplets within a few diameters of each other, the Nusselt number for the downstream droplet exhibits an entirely different character as the hot side on the droplet moves aft. Correlations of drag coefficients are reported for droplets of identical initial size. A general understanding is obtained about the modifications of droplet heating, vaporization, and drag due to the proximity of the two droplets.

Venturi Scrubber Optimization Revisited

A previous paper of ours on venturi scrubber optimization used a model by Calvert et al. to describe particle collection. Several assumptions in this model are improved in the present work; actual values for droplet drag coefficient are used rather than the Ingebo approximation, and the actual scrubber geometry is used rather than assuming the scrubber is a duct infinitely long and constant in diameter. Results from the present model suggest that the scrubber geometry affects the effectiveness with which liquid is utilized and the effectiveness with which energy is utilized. Furthermore, the conditions necessary to obtain optimum venturi performance change with particle diameter, throat velocity, and scrubber geometry. With these results, the conditions necessary for theoretically optimum performance of the scrubber can be readily identified.

Paper 9: Theoretical and Experimental Studies of Wet Steam Erosion in a Counter-Rotating Radial Steam Turbine

Erosion test in a model counter-rotating radial flow turbine has been performed to assist in the design of a 460-MW radial flow turbine. Three rows of erosion specimens were inserted at different radial locations in the last blade ring upstream of the blades to investigate the influence of the radial distance between the stages. Results showed that small droplets were formed and that erosion diminished with increased radial spacing up to a certain distance. A theoretical model for calculating droplet trajectories, sizes, and impact velocities has been derived, taking full account of wake velocity, variable droplet drag coefficient, and atomization. The calculations explained all the experimental facts and made it possible to convert the model test results to the full-size turbine showing no risk of erosion in the latter.