Development of empirical correlations to predict the secondary droplet size of impacting droplets onto heated surfaces

The present article reports an experimental analysis of the mechanisms of secondary atomization which occur at the impact of individual droplets onto heated targets. The experiments follow those reported in a previous article (Moreira et al. 2007) and encompass the use of different liquids and impact conditions. An image analysis system is combined with a phase Doppler interferometer to measure extended size distributions, which cover the full range of diameters generated at all heat transfer regimes. The results evidence that disintegration mechanisms depend on the heat transfer regimes; therefore, a universal relation cannot be devised for the outcome of droplet impact. Analysis shows that droplets impacting within the nucleate-boiling regime break-up by a thermal-induced mechanism associated with the vapour pressure at bubble nucleation sites, combined with liquid surface tension. On the other hand, within the film-boiling regime, disintegration is associated with radial disruption of the rim at the early instants after impact, as in non-heated targets, and with the rupture of the ligaments of the cellular structures. Functional relations available at the literature, mostly developed for impacts onto non-heated surfaces, are well fitted to the experimental results obtained within the film-boiling regime, since the break-up mechanisms are qualitatively similar. On the other hand, such relations cannot predict the secondary atomization occurring within the nucleate-boiling regime, as the break-up mechanisms within this regime have significantly different characteristics. In this context, the present article recognizes the relevance of the relations devised for ‘cold impacts’, to fit the size of secondary droplets within the film-boiling regime, as the correlation formulated here has a similar form: SMD/D ₀ = f(We, Re) ~ A ₁ We _N ^?0.6 Re ^?0.23 and proposes a new correlation for impacts within the nucleate-boiling regime: SMD/D ₀ = f(We, Re, Ja) ~ A ₂ We _N ^?0.14 Re ^?011 Ja ^?03. These correlations are observed to hold for impacts onto rough surfaces with dimensionless roughness R _a/D ₀ smaller than 2E-3, but not for larger roughness amplitudes, for which the data are quite scattered.     

表面形貌对滑动接触界面摩擦行为的影响

为了研究表面形貌对拉延形成的滑动接触界面摩擦行为的影响,设计了一种新型的摩擦试验装置.在油润滑条件下,针对具有单向沟槽、规则圆形凹坑和随机表面的铝合金试样,以不同滑动速度与接触压力进行一系列摩擦试验.利用非接触式三维轮廓仪测量出试验前后试样的三维表面形貌参数,并选取表面高度算术平均偏差Sa,表面支承指数Sbi,中心区空体体积Vvc和谷区空体体积Vvv来分析滑动接触界面表面形貌的变化规律.结果表明:规则圆形凹坑表面比单向沟槽表面和随机表面具有较低的摩擦系数;在相对低的接触压力下,3种表面的摩擦系数随着接触压力的增大而减小,但在高的接触压力下,3种表面的摩擦系数随着接触压力的增大而增大;在接触压力一定的情况下,3种表面的摩擦系数对滑动速度有显著依赖性;表面形貌、滑动速度和接触压力是影响滑动接触界面摩擦行为的重要因素.     

Atomization of liquid droplets on surfaces exposed to moving shock waves

Many engineering applications involve the stripping of liquid droplets from surfaces, one example being the entrainment of surface fuel from the inlet valves, ports, cylinder walls and piston crowns of internal combustion engines during the induction process. This configuration is likely to exhibit differences from the more commonly studied case of suspended droplets. In order to study the atomization of liquids from surfaces, shock waves at low Mach numbers (M = 1.05 and 1.12) have been used in the present work to initiate the flow over water droplets with visualization obtained from shadowgraph photographs, high-intensity flash photography and a CCD camera. Visualization paths both normal and angled at ±45° to the flow were used in order to obtain improved examination of the atomization details. Surface wave formation and a specific pattern of droplet distortion followed by stripping, was observed. There are similarities in the processes to those of suspended droplets that are modified by the boundary layer effects. At the Weber numbers considered, a cave-like formation occurs near the wall due to surface flow around the droplet with a major liquid flow directed tangentially across the air flow towards the cave peak where bag or chaotic type break-up and stripping takes place.     

A numerical study on droplet-particle collision dynamics

The impact of liquid droplets onto spherical stationary solid particles under isothermal conditions is simulated. The CFD model solves the Navier-Stokes equations in three dimensions and employs the Volume of Fluid Method (VOF) coupled with an adaptive local grid refinement technique able to track the liquid-gas interface. A fast-marching algorithm suitable for the quick computation of distance functions required during the grid refinement in large 3-D computational domains is proposed. The numerical model is validated against experimental data for the case of a water droplet impact onto a spherical particle at low We number and room temperature conditions. Following that, a parametric study is undertaken examining (a) the effect of Weber number (= ρu²D_o/σ) in the range of 8 to 80 and (b) the droplet to particle size ratio ranging in-between 0.31 and 1.24, on the impact outcome. This has resulted to the identification of two distinct regimes that form during droplet-particle collisions: the partial/full rebound and the coating regimes; the latter results to the disintegration of secondary satellite droplets from elongated expanding liquid ligaments forming behind the particle. Additionally, the temporal evolution of variables of interest, such as the maximum dimensionless liquid film thickness and the average wetting coverage of the solid particle by the liquid, have been quantified. The present study assists the understanding of the physical processes governing the impact of liquids onto solid spherical surfaces occurring in industrial applications, including fluid catalytic cracking (FCC) reactors.     

Thermal convection in a porous layer: Effects of anisotropy and surface boundary conditions

The theory describing the onset of convection in a homogeneous porous layer bounded above and below by isothermal surfaces is extended to consider an upper boundary which is partly permeable. The general boundary condition p + λ ∂p/∂n = constant is applied at the top surface and the flow is investigated for various λ in the range 0 ⩽ λ < ∞. Estimates of the magnitude and horizontal distribution of the vertical mass and heat fluxes at the surface, the horizontally-averaged heat flux (Nusselt number) and the fraction of the fluid which recirculates within the layer are found for slightly supercritical conditions. Comparisons are made with the two limiting cases λ → ∞, where the surface is completely impermeable, and λ = 0, where the surface is at constant pressure. Also studied are the effects of anisotropy in permeability, ξ = K _H /K _V , and anisotropy is thermal conductivity, η = k _H /k _V , both parameters being ratios of horizontal to vertical quantities. Quantitative results are given for a wide variety of the parameters λ, ξ and η. In the limit ξ/η → 0 there is no recirculation, all fluid being converted out of the top surface, while in the limit ξ/η → ∞ there is full recirculation.     

Scale-adaptive simulation of flow past wavy cylinders at a subcritical Reynolds number

The Xu & Yan scale-adaptive simulation (XYSAS) model is employed to simulate the flows past wavy cylinders at Reynolds number 8 × 10 3.This approach yields results in good agreement with experimental measurements.The mean flow field and near wake vortex structure are replicated and compared with that of a corresponding circular cylinder.The effects of wavelength ratios λ/D m from 3 to 7,together with the amplitude ratios a /D m of 0.091 and 0.25,are fully investigated.Owing to the wavy configuration,a maximum reduction of Strouhal number and root-meansquare (r.m.s) fluctuating lift coefficients are up to 50% and 92%,respectively,which means the vortex induced vibration (VIV) could be effectively alleviated at certain larger values of λ/D m and a /D m.Also,the drag coefficients can be reduced by 30%.It is found that the flow field presents contrary patterns with the increase of λ/D m.The free shear layer becomes much more stable and rolls up into mature vortex only further downstream when λ/D m falls in the range of 5-7.The amplitude ratio a /D m greatly changes the separation line,and subsequently influences the wake structures.     

Reynolds Number Dependence of Velocity Structure Functions in a Turbulent Pipe Flow

Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR _λ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized second-order structure functions show a continuous evolution withR _λ. In particular, the scaling exponentζ _v , corresponding to the v structure function, continues to increase with R _λ in contrast to the nearly unchanged value of ζ _u . The Kolmogorov constant for δu shows a smaller rate of increase with R _λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR _λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the centreline of a fully developed channel flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Critical heat flux and nucleate boiling on several heterogeneous wetting surfaces: Controlled hydrophobic patterns on a hydrophilic substrate

We used a heating surface composed of a hydrophilic substrate with hydrophobic dots to characterize the effect of spatially-different surface characteristics on critical heat flux (CHF) and nucleate boiling. To ascertain important surface factors that control CHF and boiling on heterogeneous wetting surfaces, we adjusted the hydrophobic dot diameter and the relative pitch between adjacent dots. Based on the dynamics of bubbles on hydrophobic dots, we analyze the trend of CHF on differently-fabricated heterogeneous wetting surfaces. CHFs on heterogeneous wetting surfaces were strongly dependent on ratio R of the area covered by hydrophobic dots to the heated area, but independent on the diameter of hydrophobic dots and the pitch distance. The improvement of boiling heat transfer (BHT) varied according to the conditions, and appeared to be related to the diameter, pitch distance and the number of hydrophobic dots, but the effect of R on BHT was negligible. Based on this study, we propose optimized conditions of a hydrophobic patterned surface. To sustain high CHF of a hydrophilic surface and high BHT of a hydrophobic surface, numerous micron-size hydrophobic dots should be fabricated with small R.     

Numerical and Experimental Investigation of Liquid Residue in 90° Bend Microchannel Based on Gas–Liquid Two-Phase Flow

The microfluidic chip for nucleic acid detection in vitro is an essential application of microfluidic technology to the process of in vitro diagnosis. The 90° bend microchannels in chip designed for facilitating assay reagent delivery may cause reagent residues and cast mutual contamination between detection reagents, which significantly affects the detection accuracy. In this paper, a two-dimensional gas–liquid two-phase flow model is constructed to simulate the liquid residue phenomenon. Using the results of simulation, the residual liquid generation can be observed and the area of residual liquid can be obtained. The accuracy of the numerical simulation is verified by comparison with the experimental results. The effects of the fillet radius R, the diameter ratio d₁/d₂ of the vertical to horizontal sections, the flow velocity v, and the surface roughness R_a on the residual amount are studied. We find that the fillet radius is inversely proportional to the residual amount within the range v = 20–100 mm/s and there is almost no liquid residue in the channel when the radius increases to R = 1 mm. When the channel diameter ratio d₁/d₂ increases, the liquid residual amount also increases by approximately 98%. The increased surface roughness R_a significantly increases the residual amount. The results of this study provide a reference for the optimal design of microchannels on chips.

     

Use of Faraday instabilities to enhance fuel pulverisation in air-blast atomisers

The atomization of liquids into a spray is an important process in many industrial applications and particularly in the aero-engine sector. Conventional air-blast injectors in aircraft engines today use aerodynamic shearing effects to atomize the liquid fuel. However, at operating conditions where the air velocity is below 30 m/s (such as ground start and high altitude restart) the atomization quality is poor. Consequently combustion is less efficient with high pollutant emissions. The objective of this study is to validate a new concept of injector which couples the shearing effects with the principle of ultrasonic atomization. The latter consists of using piezoelectric actuators to generate the oscillations of a wall in contact with the liquid film. This excitation perpendicular to the liquid film surface creates Faraday instabilities at the liquid/air interface. Amplitudes higher than a defined threshold value induce the break-up of ligaments and the formation of droplets. To cite this article: M. Boukra et al., C. R. Mecanique 337 (2009).     

标准超声振动气蚀孕育期内材料响应与表面形貌

材料在气蚀孕育期内仅发生极轻微的磨损,但以弹/塑性变形和晶粒拔出等方式对气蚀做出响应,具体的响应方式则随材料种类而不同.通过对孕育期内材料响应和磨损表面形貌的研究,探索不同材料响应与磨损表面形貌的关系,从而建立以表面粗糙度测量和光学显微镜观察等方式进行材料孕育期的研究.本文在标准超声振动气蚀试验机上进行了纯铜、镍基合金Hastelloy C-276和Sialon陶瓷共三种材料的气蚀试验,着重考察了它们在各自孕育期内的表面粗糙度参数（表面粗糙度R_a和核心粗糙度深度R_k）以及蚀坑面积比的变化.研究结果表明：纯铜和Hastelloy C-276在孕育期内主要以塑性变形为主.R_k不仅可以更好地反映孕育期乃至整个气蚀过程的材料表面形貌变化,还能反映不同金属在孕育期内塑性变形的程度.Sialon陶瓷在孕育期内以新蚀坑的形成为主,伴随着少量蚀坑的长大,蚀坑面积比很好地表征了陶瓷材料孕育期的变化.     

Simulation of liquid solvent atomization in compressed CO2

The work investigates numerically the atomization regime of a liquid injected into compressed CO₂ under subcritical conditions, i.e. below the CO₂-solvent critical pressure. To vary the conditions within the atomization regime whilst keeping up with realistic experimental background, ethanol and methylene chloride were selected as injected fluid and pressure was modified as well. Results first show that the jet indeed breaks up by atomization, which confirms the validity at high pressure of the breakup classification diagram. Aiming at evaluating the size distribution of the droplets formed by the jet atomization, two methods of interface tracking were investigated. Compared to the VOF-PLIC classical method, the novel sub mesh (VOF-SM) approach allows for determining smaller sized droplets without digital broadcasting.     

Interaction of a shock front with a wavy contact discontinuity

The excitation of Richtmayer-Meshkov instability fora ₀^–1>1 (a ₀ are the amplitude and wavelength of the initial contact discontinuity) is experimentally and numerically investigated. The effect of the curvature of the initial contact discontinuity on the development of the instability is determined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 168–174, September–October, 1992.     

Zweidimensionale Bestimmung des Wirkungsgrades zylindrischer Rippen

Zusammenfassung Mehrdimensionale, stationäre Temperaturfelder in zylindrischen Körpern mit rechteckigem oder kreisförmigem Querschnitt lassen sich durch Potentialfunktionen beschreiben, wenn man von den bei konvektivem Wärmeübergang üblichen Voraussetzungen ausgeht. Aus den Temperaturfunktionen kann man den Rippenwirkungsgrad ermitteln.

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Two dimensional determination of the efficiency of cylindrical fins

Two dimensional steady-state fields of the temperature in cylindrical fins of rectangular or circular cross-sections are discribed by potential functions. The fin-efficiency is deducted from this. Assumption is that the heat transfer coefficients are constant and that the heat-conductivity is independent of the temperature.

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Bezeichnungen a, b halbe Rippendicke - c_x, c_z Konstanten - h Rippenhöhe - m₁ Rippenparameter bei eindimensionaler Betrachtung - m, m_x, m_z Rippenparameter bei mehrdimensionaler Betrachtung - r, x, y, z Koordinaten - u m · a/2 - v m·h - A Querschnittsfläche des Stabes - F Wärmeübertragungsfläche - J₀, J₁ Besselfunktionen - R Zylinderradius - T Übertemperatur zur Umgebung - T₀, T₁, T₂ Übertemperaturen (vgl. Bild 1) - U Wärmeübertragender Rippenumfang - a Wärmeübergangskoeffizient - a _F,a _F1etc. a an den Rippenflanken - a _K a am Rippenkopf - _R ^* Rippen Wirkungsgrad ( _R füra _k=0) - Umfangswinkel (Koordinate) - Wärmeleitfähigkeit     

Temperaturverteilung in einem spiralförmig beheizten Rohr

Zusammenfassung Diese theoretische Arbeit befaßt sich mit der stationären Temperaturverteilung in einer Rohrwand, die von außen von einem oder mehreren parallelen elektrischen Heizleitern beheizt wird. Die Heizleiter sind spiralförmig auf das Rohr aufgewickelt. Innen wird das Rohr konvektiv gekühlt. Zur Lösung des Problems läßt sich die Wärmeleitgleichung in einem spiralförmigen Koordinatensystem aufstellen und dann mit der Annahme vereinfachen, daß alle Isothermen spiralförmig verlaufen. Die so erhaltene Differentialgleichung wird mit der Methode der Trennung der Variablen gelöst. Von besonderem Interesse sind die Temperaturunterschiede auf der Rohrinnenwand, die sich auf Grund der ungleichförmigen Beheizung ergeben. Die Rechnung zeigt, das man die Innenwandtemperatur als konstant annehmen darf, solange der axiale Abstand zweier Heizleiter, bei einer einfachen Wicklung also die Ganghöhe, kleiner ist als die Wandstärke des Rohres. Ist dieser Abstand jedoch doppelt so groß wie die Wandstärke, so können die Temperaturschwankungen auf der Rohrinnenwand in derselben Größenordnung sein wie die mittlere Differenz zwischen der Innenwandtemperatur und der Temperatur des strömenden Mediums.

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Temperature distribution in a helically heated tube

The paper is concerned with the steady state temperature distribution in a tube wall which is heated by one or several parallel line sources. The line sources are wound helically on the outer wall of the tube, which is internally cooled by convection. The heat conduction equation is formulated in helical coordinates and solved by the method of separation of variables. Special attention is paid to the temperature inhomogenities on the inner tube wall. It is shown that the inner tube wall can be assumed isothermal, if the axial distance between two line sources is smaller than the wall thickness. If this distance is twice as large as the wall thickness the temperature inhomogenities on the inner surface can be of the same order of magnitude as the difference between the average temperature of the inner surface and the temperature of the cooling medium.

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Formelzeichen Biot-Zahl - H Ganghöhe einer Spirale - I, K Assoziierte Bessel-Funktionen - N_jm siehe Gl. (34) - Q_L Heizleistung eines Heizleiters pro Längeneinheit - R_a, R_i Außen- und Innenradius des Rohres - T Temperatur - T=T₁–T₂ Temperaturdifferenz zwischen dem wärmsten und kältesten Punkt auf der Rohrinnenwand - T_m Temperatur des Kühlmediums im Rohr - a_j, b_j, c_j, d_j Koeffizienten in Gl. (11) - e_j Fourier-Koeffizienten in Gl. (23) - k_j Eigenwerte der Differentialgleichung - l_j=j · m Ordnung der assoziierten Bessel-Funktionen - m Zahl der Heizleiter - q Mittlere Wärmestromdichte auf der Rohrinnenwand - q_a Wärmestromdichteverteilung auf der Außenwand - r,, z Zylinderkoordinaten - s=R_a–R_i Wandstärke des Rohres - u, v, w Schraubenkoordinaten - a Wärmeübergangszahl auf der Rohrinnenwand - Wärmeleitfähigkeit der Rohrwand - _a, _r axiale und radiale Wärmeleitfähigkeit Herrn Professor Dr. P. Grassmann zum 65. Geburtstag gewidmet.     

Optimization of the deflagration to detonation transition: reduction of length and time of transition

The aim of this experimental investigation is the study of Deflagration to Detonation Transition (DDT) in tubes in order to (i) reduce both run-up distance and time of transition (L _DDT and t _DDT) in connection with Pulsed Detonation Engine applications and to (ii) attempt to scale L _DDT with λ_CJ (the detonation cellular structure width). In DDT, the production of turbulence during the long flame run-up can lead to L _DDT values of several meters. To shorten L _DDT, an experimental set-up is designed to quickly induce highly turbulent initial flow. It consists of a double chamber terminated with a perforated plate of high Blockage Ratio (BR) positioned at the beginning of a 26 mm inner diameter tube containing a “Shchelkin spiral” of BR ≈ 0.5. The study involves stoichiometric reactive mixtures of H₂, CH₄, C₃H₈, and C₂H₄ with oxygen and diluted with N₂ in order to obtain the same cell width λ_CJ≈10 mm at standard conditions. The results show that a shock-flame system propagating with nearly the isobaric speed of sound of combustion products, called the choking regime, is rapidly obtained. This experimental set-up allows a L _DDT below 40 cm for the mixtures used and a ratio L _DDT/λ_CJ ranging from 23 to 37. The transition distance seems to depend on the reduced activation energy (E _a/RT _c) and on the normalized heat of reaction (Q/a ₀ ²). The higher these quantities are, the shorter the ratio L _DDT/λ_CJ is. PACS 47.40.Rs · 47.60.+i · 47.70.Pq · 47.80.CbThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

Shear localisation with 2D viscous froth and its relation to the continuum model

Simulations of monodisperse and polydisperse (μ ₂(A) = 0.13±0.002) 2D foam samples undergoing simple shear are performed using the 2D viscous froth (VF) model. These simulations clearly demonstrate shear localisation. The dependence of localisation length on the product λV (shearing velocity V times the wall drag coefficient λ) is examined and is shown to agree qualitatively with published experimental data. A wide range of localisation lengths is found at low λV, an effect which is attributed to the existence of distinct yield and limit stresses. The general continuum model is extended to incorporate such an effect and its parameters are subsequently related to those of the VF model. A Herschel–Bulkley exponent of a = 0.3 is shown to accurately describe the observed behaviour. The localisation length is found to be independent of λV for monodisperse foam samples.     

Measurement of the temperature distribution within monodisperse combusting droplets in linear streams using two-color laser-induced fluorescence

Two-color laser-induced fluorescence can be use to perform space-averaged flying droplet temperature measurements. In this paper, the possibility to extend this technique to the measurement of the temperature distribution within a moving combusting droplet is considered and demonstrated. This technique may provide new experimental data related to the heat diffusion in liquid fuel droplets injected in high-temperature gas streams, for example, in combustion chambers. The main principles of the technique and the data reduction process are discussed, and a test on combusting a monodisperse ethanol droplets (200 m in diameter) stream is presented.Nomenclature a _i , b _i temperature sensitivity coefficients for i th spectral band - C molecular concentration of fluorescent tracer - D droplet diameter - I ₀ incident laser beam intensity - I _f fluorescence intensity - K _opt optical constant - K _spec spectroscopic constant - V _c collection volume - R _f fluorescence ratio - T absolute temperature - T _i injection temperature - V _i injection velocity - ( x, y , z) spatial coordinates Greek symbols temperature sensitivity coefficient     

On a Boundary-Value Problem of Periodic Type for First-Order Linear Functional Differential Equations

We establish unimprovable sufficient conditions for the unique solvability of the boundary-value problem