Hollow droplets impacting onto a solid surface

The impact process of spherical hollow droplets impinging onto a solid surface has been experimentally studied. Formation of a counter-jet in a wide range of Reynolds and Weber numbers was revealed, this jet being similar to a Worthington jet. For characterizing the regime of liquid flow in the hollow droplet, we propose using the Euler number. Theoretically, the problem was treated using a simple model of axisymmetric liquid flow. The obtained results proved to be consistent with experimental data.     

Pressure measurements on the impingement surface of sonic and sub-sonic jets impinging onto a flat plate at inclined angles

The flow field associated with a jet impinging onto a surface at an inclined angle is investigated using pressure-sensitive paint (PSP) and particle image velocimetry. The PSP yields continuous measurements of pressure on the jet impingement surface. The jet footprint on the impingement surface is visualized using the half-maximum pressure contour. The results indicate that the impingement angle of the jet is the dominant parameter in determining the footprint of the jet on the impingement surface. This contour is similar in shape to an ellipse that is created by projecting the nozzle through the impingement surface. The ellipse is centered at the location of maximum pressure and the width of the minor axis is just over one jet diameter. The location of maximum pressure is found upstream of the geometric impingement point and this location is a strong function of the impingement angle. A curve fit for the location of maximum pressure can be constructed using an exact solution of the Navier–Stokes equations for a non-orthogonal stagnation flow. The maximum value of pressure is a function of impingement angle and varies as the sine of the impingement angle squared; the maximum pressure is also a function of jet impingement distance. Using these results, a simple procedure for predicting the overall structure of the jet on the impingement surface is presented.     

The impingement of sonic and sub-sonic jets onto a flat plate at inclined angles

The flow field associated with a jet impinging onto a surface at an inclined angle is investigated using particle image velocimetry (PIV). The results indicate that as a free jet impinges on a flat surface at an inclined angle the jet is turned by and spread laterally onto the impingement surface. The impingement angle of the jet is the dominant parameter in determining the rate of turning/spreading for the jet. The stagnation point is located using the PIV data and is found upstream of the geometric impingement point and upstream of the location of maximum pressure. The location of the stagnation point is a strong function of impingement angle and a weak function of impingement distance and pressure ratio. The location of the stagnation point is compared with the location of maximum pressure and compared to a curve fit for the location of maximum pressure based an exact solution of the Navier–Stokes equations for a non-orthogonal stagnation flow.     

Sedimentation of a cloud of a bidispersed aerosol onto a flat horizontal surface

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 101–108, March–April, 1992.     

Effect of impingement angle on the outcome of single water drop impact onto a plane water surface

Experiments of single water drop impact onto a plane water surface were carried out to investigate the effect of impingement angle on the total mass of secondary drops produced during the collision. When the impingement angle (the angle between the velocity vector of primary drop and the normal vector to water surface) was less than 50°, an increase in the impingement angle led to a remarkable increase in the total mass of secondary drops; this could be attributed to a significant increase in the secondary drop size. However, no secondary drop was observed within the experimental ranges tested when the impingement angle exceeded 70°.     

A finite element method study of Eulerian droplets impingement models

To compute droplet impingement on airfoils, an Eulerian model for air flows containing water droplets is proposed as an alternative to the traditional Lagrangian particle tracking approach. Appropriate boundary conditions are presented for the droplets equations, with a stability analysis of the solution near the airfoil surface. Several finite element formulations are proposed to solve the droplets equations, based on conservative and non‐conservative forms and using different stabilization terms. Numerical results on single and multi‐elements airfoils for droplets of mean volume diameter, as well as for a Langmuir distribution of diameters, are presented and validated against measured values. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical investigation of the impingement of an oblique shock on a flat plate

Summary The unsteady, compressible Navier-Stokes equations in Reynolds-averaged variables are solved for a shock wave turbulent boundary layer interaction. For the free stream Mach number 3.7 and Reynolds number 8.202×10⁶ computation is performed using MacCormack's explicit-implicit finite difference scheme with 42×42 grid points. It is found that the peak heating amplification correlation agrees well with computational results.

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Numerische Untersuchung des Auftreffens einer schiefen Stoßwelle auf eine ebene Platte

Zusammenfassung Die Navier-Stokes-Gleichungen in instationärer, kompressibler Form mit Reynolds-gemittelten Variablen werden für die gegenseitige Beeinflussing einer Stoßwelle mit einer turbulenten Grenzschicht gelöst. Die Berechnung wird anhand des MacCormack's explizit-impliziten Finite-Differenzen-Verfahrens mit 42×42 Gitterpunkten für eine Freistrahl-Machzahl von 3,7 und einer Reynoldszahl von 8,202·10⁶ durchgeführt. Die Rechenergebnisse stimmen mit den Experimenten gut überein.

     

Coalescence of two droplets impacting a solid surface

Coalescence of a falling droplet with a stationary sessile droplet is studied experimentally. High-speed video images are presented to show coalescence dynamics, shape evolution and contact line movement. Emphasis is put on spread length, which is the length of two coalesced droplets along their original centers. Experimental results have shown that the spread length can be larger or smaller than the ideal spread length, which is the spread diameter of individual droplet plus the center-to-center distance between the two droplets. Three different coalescence mechanisms based on comparing the maximum and the minimum spread lengths to the ideal spread length are identified. Correlations for the maximum and the minimum spread lengths are developed, which can be combined with the coalescence domains to determine the deposition conditions for forming continuous or discontinuous lines.     

Energy distribution from vertical impact of a three-dimensional solid body onto the flat free surface of an ideal fluid

Hydrodynamic impact phenomena are three dimensional in nature and naval architects need more advanced tools than a simple strip theory to calculate impact loads at the preliminary design stage. Three-dimensional analytical solutions have been obtained with the help of the so-called inverse Wagner problem as discussed by Scolan and Korobkin in 2001. The approach by Wagner provides a consistent way to evaluate the flow caused by a blunt body entering liquid through its free surface. However, this approach does not account for the spray jets and gives no idea regarding the energy evacuated from the main flow by the jets. Clear insight into the jet formation is required. Wagner provided certain elements of the answer for two-dimensional configurations. On the basis of those results, the energy distribution pattern is analysed for three-dimensional configurations in the present paper.     

过冷水滴撞击螺旋桨桨叶表面的数值模拟

本文介绍了某型螺旋桨在不同飞行状态下.求解桨叶水滴撞击特性的数值方法.该方法对桨叶运动模型进行简化,并在对绕桨叶运动的气流场计算的基础上,采用拉格朗日方法求解气流场中水滴运动方程,得到水滴运动轨迹.进而,确定了水滴对桨叶的撞击特性参数,为桨叶防冰系统设计提供条件.主要结论如下:(1)在巡航状态下,桨叶沿展向方向上总收集系数Em和局部收集系数β不断增大;(2)在爬升状态下,随着爬升高度H不断增大,飞行速度V0不断增大,水滴撞击在桨叶表面的范围有所增加,而且β随之增大;(3)随着水滴平均有效直径(MVD)的增大,水滴撞击在桨叶表面的范围明显增加同时,β在桨叶表面同一位置的值也随之增大.     

A two-dimensional splashing model for investigating impingement characteristics of supercooled large droplets

In this article, a two-dimensional (2D) splashing model is proposed to investigate the dynamics when supercooled large droplets (SLD) impinging on a wall surface in the aircraft-icing field. Energy conservation for droplet motion and impingement is used to capture the properties of the splashed droplets. A new statistical treatment of the droplet impinging energy and angle during the droplet-wall interaction is introduced in order to calculate the average dynamics of the SLD within a micro-control volume on wall surface. Based on the LEWICE predictions of droplet collection efficiencies and the available experimental ones, a new criterion for droplet splashing/deposition as well as a new formulation for the splashed mass is suggested. Lagrangian approach is adopted to describe the movement and impingement of SLD. The proposed model together with the previously developed droplet tracking method (DTM) for calculating droplet collection efficiency with the effect of droplet reimpingement constitute a relatively complete predicting approach of SLD impingement characteristics. Comparisons between the current predictions and the experimental observations, including SLD impingement over clean and contaminated airfoil surfaces as well as shapes of ice accretion in typical icing conditions, are carried out. Further, results obtained with the LEWICE splashing model are also plotted on the same graphs in order to assess the accuracy of the current splashing model in predicting SLD impingement. Results show that good agreement is achieved between the current predictions, including SLD impingement and ice accretion shapes, and the experimental ones. The predictions of the impingement distribution over contaminated surfaces obtained with the current splashing model show a much closer agreement with the experimental results than the ones obtained with LEWICE splashing model. For further investigation of SLD impingement, the properties of the droplet splashing and reimpingement during the ice accretion process are also addressed.     

Energy balance of droplets impinging onto a wall heated above the Leidenfrost temperature

This work is an experimental study aiming at characterizing the heat transfers induced by the impingement of water droplets (diameter 80–180 μm) on a thin nickel plate heated by electromagnetic induction. The temperature of the rear face of the nickel sample is measured by means of an infrared camera and the heat removed from the wall due to the presence of the droplets is estimated using a semi-analytical inverse heat conduction model. In parallel, the temperature of the droplets is measured using the two-color Laser-Induced Fluorescence thermometry (2cLIF) which has been extended to imagery for the purpose of these experiments. The measurements of the variation in the droplet temperature occurring during an impact allow determining the sensible heat removed by the liquid. Measurements are performed at wall conditions well above the Leidenfrost temperature. Different values of the Weber numbers corresponding to the bouncing and splashing regimes are tested. Comparisons between the heat flux removed from the wall and the sensible heat gained by the liquid allows estimating the heat flux related to liquid evaporation. Results reveal that the respective level of the droplet sensible heat and the heat lost due to liquid vaporization can vary significantly with the droplet sizes and the Weber number.     

Three-dimensional numerical analysis of the deformation behavior of droplets impinging onto a solid substrate

The collision dynamics of water droplets impacting onto a solid is studied by means of three-dimensional computer simulations. The Navier–Stokes equations for unsteady, incompressible, viscous fluids in the three-dimensional Cartesian coordinate system are approximated and solved by a finite difference method. The volume-of-fluid (VOF) technique is used to track the free liquid surface. Normal and oblique collisions of droplets with the substrate are simulated at low droplet impact inertia. The effect of impact angle on the deformation behavior of droplets is investigated. The experimental observations and the numerical results are in reasonable agreement. Theoretical aspects of the physics of the collision phenomena are addressed.     

Axisymmetric impingement of a hot jet on a flat plate: equilibrium flow analysis of high-temperature air

The flow structure of an underexpanded supersonic jet with high reservoir temperature impinging on a flat plate has been numerically investigated using a Total Variation Diminishing (TVD) scheme. When the temperature of the flow field is high enough to cause chemical reaction, the specific heat ratio,, is no longer equal to 1.4, nor constant. This explains the difference found in the literature between the flow properties of the calorically perfect gas and that of the chemically reacting flow. Under the equilibrium flow assumption the effect of high temperature gas on the impinging jet has been taken into account in the present paper by using specific heat ratio and speed of sound given by correlation polynomials of thermodynamic variables. The limiting case of cold jet calculation in the present numerical results agreed well with the existing experimental data. For the equilibrium jet with high reservoir temperature,T _o=1000K, qualitative support of the present result has been provided by means of the approximation theory.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Modelling of liquid-liquid metal mixing

Mathematical and physical modelling have been used interactively to predict the behaviour of two liquid metals mixing in the nosetip of a Roll-casting machine. Attention has been given to the transient development of density driven backflows due to incomplete mixing and forward transport of fluid. The results are compared with temperature and composition data obtained from metallurgical trials.Mixing reactions which may involve a simultaneous phase change (partial solidification) are also discussed in relation to the local mixing conditions.     

Study of airborne particles produced by normal impact of millimetric droplets onto a liquid film

The aim of this work is to carry out an experimental investigation into the generation of airborne microparticles when millimetric droplets of aqueous solutions impact onto a liquid film. Impact experiments using 3.9 mm diameter droplets were carried out for Weber numbers between 159 and 808, with a fixed Ohnesorge number of 2 × 10⁻³ and film parameters S _f (the ratio between the thickness of the liquid film h _film and the diameter of the impacting droplet d _i) between 0.3 and 1. Observed results show that the deposition/splashing threshold is independent of the parameter S _f in agreement with the data in the literature. The aerosol measurement results demonstrate the production of solid particles from the evaporation of secondary microdroplets with diameters less than 30 μm formed when splash occurs. The median diameter of these microdroplets is around 20 μm, corresponding to a value of d ₅₀/d _i = 5 × 10⁻³. Taken together, the results show that the mass and the number of particles emitted increase as the Weber number increases. Moreover, at a Weber number of 808, the results show that the mass and number of particles emitted increases as the parameter S _f decreases. In this case, the mean number of microdroplets emitted per impact is equal to 14 for S _f = 1 and equal to 76 for S _f = 0.3.