Numerical investigation of boiling

In this work, we study different phenomena that occur during nucleate boiling. We numerically investigate boiling using two phase flow direct numerical simulation based on a level set / Ghost Fluid method. This method allows us to follow the interface and to make accurate geometric calculation as for bubble curvature. Nucleate boiling on a plate is not only a thermal issue, but also involves multiphase dynamics issues at different scales and at different stages of bubble growth. As a consequence, we divide the whole problem and investigate separately the different phenomena considering their nature and the scale at which they occur. First we analyse the boiling of a static bubble immersed in an overheated liquid. We perform numerical simulations at different Jakob numbers in the case of strong discontinuity of density through the interface. These simulations permit us to estimate the accuracy of our numerical method dealing with phase change in the context of two phase flow direct numerical simulation. The results show a good agreement between numerical bubble radius evolution and the theoretical evolution found by Scriven(1959). The validation of our code for the Scriven case allows to pursue our study by focusing on the phenomena that take place in the particular case of an interaction with a wall. This interaction is characterised by the angle formed between a solid and a fluid interface, named the contact angle. We implement a method that makes it possible for a droplet, to reach, in the case of a static contact angle, a steady state corresponding to a theoretical equilibrium. Besides this method enables to take into account the contact angle hysteresis model, which considers different angles whether the contact line is advancing or recoiling. We perform simulations of the spreading of a liquid droplet impacting on a plate, and we compare the maximum spreading diameter and the advancing and receding droplet behaviour of our numerical results with the experimental data Son and Lee (2010) have reported

Pool boiling in microgravity with a single specie system

Pool boiling experiments in microgravity on the small copper plate of 1cm² have been performed in the SOURCE 2 experiment aboard the sounding Rocket Maser 12 launched on February 13th, 2012. The SOURCE 2 experiment is a small-scale tank devoted to the study of heat and mass transfers with a liquid refrigerant HFE7000 pressurised with its vapour. SOURCE 2 (SOUnding Rocket Compere Experiment) was developed in the frame of a French German space programme COMPERE (on the behaviour of propellant in launcher tanks) managed by CNES and DLR and a MAP ESA Project "Multiscale Analysis of boiling". During the 6 minutes of the flight different physical phenomena were studied by our partners: ZARM, University of Bremen, Air Liquide and Astrium. The boiling experiment was performed in a 6 cm diameter and 28 cm long cylindrical tank partly filled with a refrigerant Novec HFE7000 with a low boiling point (34°C at 1 bar) and pressurized by its own vapour. The heating element used for the boiling investigation consisted of an electrical resistance heated by Joule effect in contact with a flux-meter and a copper plate with a thickness of 40 micrometres. The flux-meter was equipped with two thermocouples. It was then possible to measure at the same time the heat flux transmitted to the liquid and the wall temperature. The liquid temperature above the heater was measured by 5 micro thermocouples located in the vicinity of the wall. Images of the boiling phenomenon were recorded by a video camera through the transparent cylindrical wall of the tank. SOURCE 2 is in the continuity of the SOURCE 1 experiment, which flew successfully on Maser 11 on 15 May 2008 (Kannengieser et al. 2010). The experiment scenario was similar to the present case. However, in SOURCE 1, liquid HFE-7000 was pressurized by gaseous nitrogen. The lateral glass wall was preheated and a strong evaporation took place at the free surface in the vicinity of the wall. Due to the presence of nitrogen a strong Marangoni convection occurred at the free surface enhancing nitrogen dissolution in the liquid phase. Then during the boiling experiment, the bubble growth was due to liquid vaporization and nitrogen desorption. Marangoni convection also occurred at the bubble interface leading to a capillary force pushing the bubble to the heated wall. In the SOURCE 2 experiment, a single specie configuration is studied (liquid/vapour HFE7000). This changes the thermo-hydraulic behaviour of the system. Since no Marangoni convection kept the bubble in contact with the heated wall, a primary bubble detached and grew by feeding itself with the smaller bubbles formed over the heated surface. The change in the bubble size is only due to vaporization. Then the measurements of the heat flux transferred to the fluid by the heater could be directly correlated to the amount of vapour production (balance of evaporation and re-condensation) that could be evaluated from visualization and image processing. When the rocket was launched, the test cell was empty. The top part and the lateral glass wall of the test cell were preheated before launch. Just before the microgravity period, the tank filling began, liquid HFE7000 at 25 °C was injected in the tank by the pump and pressurized by hot vapour HFE7000. At the beginning of the boiling experiment, the tank pressure was reduced to 1.5 bars and the heating of the heater element was switch on and boiling started. During this period, it was planed to study boiling with high sub-cooled liquid then to decrease the pressure to 1 bar to study saturated boiling. However while pressurization with hot vapour HFE7000, strong condensation occurred that rapidly warmed up HFE7000 up to 40°C during boiling study. As a consequence, at 1.5 bars, the sub-cooling was limited to 5 degrees. Then the tank pressured was reduced to 1.3 bars to investigated boiling in saturated conditions. On the other hand, before launch, tests were performed on ground and boiling curves were plotted. In this paper we will attend to compare the results obtained in micro-gravity and in 1G

Effect of rising motion on the damped shape oscillations of drops and bubbles

The objective of this work is to determine the effect of the rising motion on the dynamics of inertial shape oscillations of drops and bubbles. We have carried out axisymmetric direct numerical simulations of an ascending drop (or bubble) using a level-set method. The drop is initially elongated in the vertical direction and therefore performs shape oscillations. The analysis is based on the decomposition of the inter- face into spherical harmonics, the time evolutions of which are processed to obtain the frequency and the damping rate of the oscillations. As the drop accelerates, its shape flattens and oscillations no longer take place around a spherical equilibrium shape. This causes the eigenmode of oscillations to change, which results in the ap- pearance of spherical harmonics of high order that all oscillate at the same frequency. For both drops and bubbles, the frequency, which remains controlled by the potential flow, slightly decreases with the rising velocity. The damping rate of drops, which is controlled by the dissipation within boundary layers at the interface, strongly in- creases with the rising velocity. At terminal velocity, the damping rate of bubbles, which results from the dissipation by the potential flow associated with the oscillating motion, remains close to that of a non-rising bubble. During the transient, the rate of deformation of the equilibrium shape of bubbles can be comparable to the oscillation frequency, which causes complex evolutions of the shape. These results extend the description of shape oscillations to common situations where gravity plays a role. In particular, the present conclusions are useful to interpret experimental results where the effect of the rising motion is often combined with that of surfactant

Solving elliptic problems with discontinuities on irregular domains – the Voronoi Interface Method.

We introduce a simple method, dubbed the Voronoi Interface Method, to solve Elliptic problems with discontinuities across the interface of irregular domains. This method produces a linear system that is symmetric positive definite with only its right-hand-side affected by the jump conditions. The solution and the solution's gradients are second-order accurate and first-order accurate, respectively, in the L∞L∞ norm, even in the case of large ratios in the diffusion coefficient. This approach is also applicable to arbitrary meshes. Additional degrees of freedom are placed close to the interface and a Voronoi partition centered at each of these points is used to discretize the equations in a finite volume approach. Both the locations of the additional degrees of freedom and their Voronoi discretizations are straightforward in two and three spatial dimensions

Direct numerical simulation of nucleate boiling in micro-layer regime

The physical mechanisms associated with the evolution of a micro-layer beneath a bubble and the transition between contact line and micro-layer regimes are investigated with fully resolved numerical simulations, in the framework of nucleate pool boiling. Capturing the transition between these two regimes has been possible for the first time using very refined grids and parallel computations. Indeed, grids with a cell size under 1 l m must be used in order to capture thermal and dynamical effects in the micro-layer. Such multiscale computations require advanced code capabilities. The present simulations are used to analyse the physical processes involved in the formation and depletion of a micro-layer. A parametric study is carried out to investigate the impact of the main parameters affecting the presence of the micro-layer. From these results, the limit conditions between nucleate boiling in micro-layer and contact line regimes are deduced. Neglecting the micro-layer would lead to erroneous results because it has a strong influence on the overall bubble growth. Therefore the present results could be of major interest for designing models of nucleate pool boiling in larger scales computations, when the micro-layer cannot be resolved

Direct numerical simulation of nucleate pool boiling at large microscopic contact angle and moderate Jakob number

International audienceIn this paper, we present Direct Numerical Simulations of Nucleate Boiling on a single site in configurations involving both a large microscopic contact angle, a moderate Jakob number (less than 50) and a high density ratio between the two phases. A detailed study on the validation of the numerical simulations is presented. Several issues about the numerical modelling of the contact line are addressed in order to define a global strategy to perform accurate and predictive simulations. Benchmarks from pioneering studies (Son et al., 1999) have been reproduced with more recent numerical methods and thinner grids in order to define the most relevant strategy for successful simulations. In particular, the grid sensitivityof the solution is thoroughly investigated by performing simulations with four successive grids. The numerical results are compared favorably with experimental data, since the discrepancy between the numerical solutions and the experimental data is always less than 10% whether the departure diameter or the departure frequency are considered. The influence on the numerical solution of the thermal con duction in the solid heater is also assessed and we report that this parameter has no influence in the con figurations of thick and highly conductive materials that have been considered in this study. We also present clarifications about the requirement of a specific modelling in the contact line region in order to account for a possible impact of the micro-region. Finally, based on the results of this analysis of our numerical simulations, we formulate the following unusual conclusion: the implementation of a micro-region model and an additional coupling between the overall solver and such a model is not required to perform well-resolved and accurate numerical simulations in the case of high density ratio,high microscopic contact angle (up to 30°) and moderate Jakob number. Next, we present some compar isons on the bubble shape evolution between the numerical simulations and a static force balance model, in order to investigate the mechanisms leading to the bubble detachment. Finally, we conclude this paper by presenting a parametric study, by varying the Jakob number, in order to propose a new correlation on the bubble detachment radius depending on the latter dimensionless number

A Ghost Fluid/Level Set Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect.

The development of numerical methods for the direct numerical simulation of two-phase flows with phase change, in the framework of interface capturing or interface tracking methods, is the main topic of this study. We propose a novel numerical method, which allows dealing with both evaporation and boiling at the interface between a liquid and a gas. Indeed, in some specific situations involving very heterogeneous thermodynamic conditions at the interface, the distinction between boiling and evaporation is not always possible. For instance, it can occur for a Leidenfrost droplet; a water drop levitating above a hot plate whose temperature is much higher than the boiling temperature. In this case, boiling occurs in the film of saturated vapor which is entrapped between the bottom of the drop and the plate, whereas the top of the water droplet evaporates in contact of ambient air. The situation can also be ambiguous for a superheated droplet or at the contact line between a liquid and a hot wall whose temperature is higher than the saturation temperature of the liquid. In these situations, the interface temperature can locally reach the saturation temperature (boiling point), for instance near a contact line, and be cooler in other places. Thus, boiling and evaporation can occur simultaneously on different regions of the same liquid interface or occur successively at different times of the history of an evaporating droplet. Standard numerical methods are not able to perform computations in these transient regimes, therefore, we propose in this paper a novel numerical method to achieve this challenging task. Finally, we present several accuracy validations against theoretical solutions and experimental results to strengthen the relevance of this new method

A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves

This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48], a preconditioning explicit HLLC solver [14] and the compressible projection method , and , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered. Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation

Direct numerical simulations of droplet condensation

We present in this work well-resolved and accurate Direct Numerical Simulations (DNS) of droplet condensation. Despite the great scientific and industrial interest, to this day, there is not an extensive knowledge of the different processes involved in droplet condensation. Consequently, DNS should be considered as a promising tool to investigate on this phenomenon. A preliminary validation of our simulations is carried out by direct comparison with the quasi-static theory of the droplet condensation in an infinite vapour medium. Next, more complex configurations have been considered: the condensation of a moving droplet in a subcooled vapour flow and the condensation of a hemispherical droplet deposed on an isothermal flat surface. The latter represents a first step towards the understanding of the more demanding DropWise Condensation. In both configurations, the effects of the Jakob number, Ja, have been thoroughly analysed to understand how the condensation impacts on the droplet heat flux and dynamics. This has led to the definition of a particular condensation regime for the lower Ja values, hereinafter called low condensation rate regime, where the droplet heat transfer is independent of the Ja. By increasing the Ja, instead, the effects due to condensation start to grow exponentially. This regime is referred as the high condensation rate regime in this paper. Finally, some general trends for correlations on the Nusselt number and drag coefficient accounting for condensation are proposed in this study