Mario F. Trujillo

Modelling and experiment of impingement and atomization of a liquid spray on a wall

Abstract An experimental and computational investigation of spray impingement on a flat surface is presented. Different angles of incidence are studied, namely 30, 45 and 60°C measured from the normal to the surface. Back-lit photographs of the wall spray taken at various times during the impingement period give a qualitative view of the secondary atomization process. A stochastic model based on the sampling of velocity and size distributions of secondary droplets is used to simulate the creation of incident droplet fragments created by the numerous splashing events occurring during the impingement period. Size characteristics of the secondary droplet cloud are computed at various points in the impingement region and these are compared against phase/Doppler particle analyser (P/DPA) measurements yielding reasonable agreement. The effect of surface roughness is incorporated into the model and is found to play a major role in affecting the splashing threshold and the sizes of splashing fragments. The secondary droplet distributions are virtually unchanged among the different angles of incidence. This behaviour is explained by considering the shift in the splashing droplet distribution as a function of incident angle.

Numerical Simulations and Experimental Characterization of Heat Transfer From a Periodic Impingement of Droplets

In this combined experimental and simulation investigation, a stream of HFE-7100 droplets striking a prewetted surface under constant heat flux was studied. An implicit free surface capturing technique based on the Volume-of-Fluid (VOF) approach was employed to simulate this process numerically. Experimentally, an infrared thermography technique was used to measure the temperature distribution of the surface consisting of a 100 nm ITO layer on a ZnSe substrate. The heat flux was varied to investigate the heat transfer behavior of periodic droplet impingement at the solid–liquid interface. In both experiments and simulations, the morphology of the impact zone was characterized by a quasi-stationary liquid impact crater. Comparison of the radial temperature profiles on the impinging surface between the experiments and numerical simulations yielded reasonable agreement. Due to the strong radial flow emanating from successive droplet impacts, the temperature distribution inside the crater region was found to be significantly reduced from its saturated value. In effect, the heat transfer mode in this region was governed by single phase convective and conductive heat transfer, and was mostly affected by the HFE-7100 mass flow rates or the number of droplets. At higher heat fluxes, the minimum temperature, and its gradient with respect to the radial coordinate, increased considerably. Numerical comparison between average and instantaneous temperature profiles within the droplet impact region showed the effect of thermal mixing produced by the liquid crowns formed during successive droplet impact events. [DOI: 10.1115/1.4004348]

Modeling crown formation due to the splashing of a droplet

The typical crown formation created by the impact of a single drop on a slightly wetted target surface is treated as a series of two surfaces of discontinuity from which the jump momentum and mass equations are developed along with the governing equation for crown radius. The crown radius equation is solved in conjunction with the governing equations of the flow emanating from drop/wall impact. This flow is modeled initially as a cylindrical region of prescribed height and velocity. Both viscid and inviscid situations are treated. For the inviscid case of a crown moving through a motionless film, analytical solutions are found for the evolution of film height and velocity. For the viscid situation, a numerical scheme based on the discretization of the governing equations along the characteristic directions is employed. The results are validated by comparing with experimental and computational results from the literature. The effects of target surface film height, velocity, and wall friction on the crown dynamics are investigated.

Thermal boundary layer analysis corresponding to droplet train impingement

Simulations of droplet train impingement on a pre-wetted solid surface heated from below are used to study the thermal boundary layer behavior over a parameter space which includes variations in Reynolds, Peclet, and Weber numbers, as well as variations in inter-droplet spacing and initial liquid film thickness. Computationally, a modified version of the Volume-of-Fluid method is developed and employed in this study. The solver is validated against closed form solutions and additional experimental data from the literature. In combination with the simulations, an analytical representation is also developed and compared to the computations yielding favorable agreement. Results show that the boundary layer thickness is mostly affected by changes in inter-droplet spacing, Reynolds, and Peclet number, and influenced minimally by variations in Weber number and initial film thickness. In fact, it is explicitly demonstrated in the analysis that the impact velocity has the greatest effect in local heat transfer. A...

Distinguishing features of shallow angle plunging jets

Numerical simulations employing an algebraic volume-of-fluid methodology are used to study the air entrainment characteristics of a water jet plunging into a quiescent water pool at angles ranging from θ = 10° to θ = 90° measured from the horizontal. Our previous study of shallow angled jets [S. S. Deshpande, M. F. Trujillo, X. Wu, and G. L. Chahine, “Computational and experimental characterization of a liquid jet plunging into a quiescent pool at shallow inclination,” Int. J. Heat Fluid Flow 34, 1–14 (2012)]10.1016/j.ijheatfluidflow.2012.01.011 revealed the existence of a clearly discernible frequency of ingestion of large air cavities. This is in contrast with chaotic entrainment of small air pockets reported in the literature in case of steeper or vertically plunging jets. In the present work, the differences are addressed by first quantifying the cavity size and entrained air volumes for different impingement angles. The results support the expected trend – reduction in cavity size (D43) as θ is incre...

A computational study of an atomizing liquid sheet

Linear instability predictions of liquid sheets injected into a gas medium are well established in the literature. These analyses are often used in Lagrangian-Eulerian spray simulations, a prominent simulation method, to model the dynamics occurring in the near-nozzle region. In the present work, these instability predictions are re-examined by first generalizing the treatment of interfacial conditions and related assumptions with a two-phase Orr-Sommerfeld (OS) system, and second, by employing highly resolved-Volume-of-Fluid (VoF) simulations. After presenting some validation exercises for both the VoF and OS solvers, the OS predictions are compared to earlier studies from the literature leading to reasonable agreement in the limit as the boundary layer thickness tends to zero. Results from VoF simulations of liquid sheet injection are used to characterize the range of scales of the liquid structures immediately before atomization. The mean value in this range is found to be approximately two to three orders of magnitude larger than the corresponding predictions from previous studies. A two-phase mixing layer under the same physical conditions is used to examine this disparity, revealing that within the linear regime, relatively good agreement exists between the VoF and OS predicted instability mechanisms. However, the most unstable mode in the linear regime is too small to cause a fracture or atomization of the liquid sheet and hence cannot be directly responsible for the atomization. The generation of a much larger mode, which emerges well beyond the linear regime, is the one causing breakup.

Modeling Urea-Water Solution Droplet Evaporation

A computational solver has been developed for the calculation of urea-water-solution (UWS) droplet vaporization. It is based on the solution of the mass density, chemical species transport, and energy within the droplet, and it is fully coupled to the jump conditions for species and energy transport at the droplet interface, and the phase-equilibrium conditions. Pressure-volume-temperature relationships and fugacities are predicted using the Peng-Robinson equation of state. The numerical code is validated by testing its ability to resolve the dynamics of internal species and temperature fields during phase change, predict phase equilibrium for UWS and hydrocarbon systems, and predict vaporization for C 7H16, C 7H16/C 10H22, and UWS droplets. Results show that UWS droplet vaporization can be divided into three different phases consisting of (i) temperature rise at nearly constant composition, (ii) overall urea enrichment at nearly constant temperature, and (iii) simultaneous overall heating and urea enrichment of the entire droplet. The third phase is typically characterized by solidification of the gas-liquid interface, producing a urea shell, a state that can potentially lead to micro-explosions. Higher ambient temperatures are shown to promote urea solidification more readily than lower temperatures to the decreasing role of liquid species diffusion with increasing temperature.

Generalizing the Thermodynamics State Relationships in KIVA-3V

The Peng-Robinson equation of state has been implemented into the KIVA-3V code to better handle high-pressure conditions typical of Diesel engine environments. The implementations modify pressure-volume-temperature relationships, specific heats, and departures in internal energy, among other thermodynamic partial derivatives. Computations show that significant deviations do occur for progressively heavier hydrocarbons. However, when these hydrocarbons exist in a mixture with a non-negligible portion of air, the departures from ideal behavior are mitigated. Internal energy calculations have been extended to allow for pressure effects, but the strongest factor continues to be temperature. Hence departures from ideal behavior in internal energy and related specific heats are minimum.

Film dynamics relevant to spray cooling

For a number of years spray cooling has shown to be a viable alternative for thermal management of high-density electronics. Nevertheless, the key fundamental physical processes are to a large degree poorly understood due mostly to the complicated fluid dynamics resulting from nucleate boiling coupled with spray drop impingement. In this combined experimental and modeling effort, a representative configuration consisting of a liquid film resting on a solid silicon-based substrate with an imposed constant heat flux and an impinging train of droplets has been studied. This configuration mimics to a great degree the physics of spray cooling, while simultaneously simplifying the experimental and computational analysis to a manageable level. It is shown that a number of statistically quasi-stationary states are possible by carefully coordinating the heat flux and drop impingement rates. Studies were both performed for water and FC-72. Due in part to its lower surface tension, the quasi-stationary states for FC-72 were instantaneously much more chaotic than the corresponding water cases. The OpenFoam (open source computational fluid dynamics) code has been supplemented with an energy equation within the existing Volume-of-Fluid infrastructure. This was used to analyze the dynamics in the impingement region. It is shown that the temperature in this region is approximately equal to the temperature of incident droplets. For all water and FC-72 films, it was found that each droplet impact penetrated the entire thickness of the film bringing a significant cooling effect on the heated substrate. This was the case even for film thickness-to-impact droplet diameter ratios far exceeding one.

Gradient Augmented Level Set Method for Phase Change Simulations

Abstract A numerical method for the simulation of two-phase flow with phase change based on the Gradient-Augmented-Level-set (GALS) strategy is presented. Sharp capturing of the vaporization process is enabled by: i) identification of the vapor–liquid interface, Γ ( t ) , at the subgrid level, ii) discontinuous treatment of thermal physical properties (except for μ), and iii) enforcement of mass, momentum, and energy jump conditions, where the gradients of the dependent variables are obtained at Γ ( t ) and are consistent with their analytical expression, i.e. no local averaging is applied. Treatment of the jump in velocity and pressure at Γ ( t ) is achieved using the Ghost Fluid Method. The solution of the energy equation employs the sub-grid knowledge of Γ ( t ) to discretize the temperature Laplacian using second-order one-sided differences, i.e. the numerical stencil completely resides within each respective phase. To carefully evaluate the benefits or disadvantages of the GALS approach, the standard level set method is implemented and compared against the GALS predictions. The results show the expected trend that interface identification and transport are predicted noticeably better with GALS over the standard level set. This benefit carries over to the prediction of the Laplacian and temperature gradients in the neighborhood of the interface, which are directly linked to the calculation of the vaporization rate. However, when combining the calculation of interface transport and reinitialization with two-phase momentum and energy, the benefits of GALS are to some extent neutralized, and the causes for this behavior are identified and analyzed. Overall the additional computational costs associated with GALS are almost the same as those using the standard level set technique.