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A multi-component multi-phase thermal lattice Boltzmann model considering vapor-liquid phase change is developed to study droplet condensation with the presence of non-condensable gas. Some tests, including an isolated droplet evaporation, are conducted to verify the capability of this model in simulating multi-component multi-phase flow with vapor-liquid phase change. After that, single droplet condensation considering non-condensable gas is investigated with different mass fraction of non-condensable component and contact angles. The results show that the influence of the non-condensable gas upon droplet condensation heat transfer is depended on the growth stage and the amount of the non-condensable gas. The mass transfer of vapor and non-condensable component will tend to an equilibrium state with the droplet condensation going. Furthermore, for different contact angles, the dynamic behavior of the contact line plays a critical role in the accumulation effect of the non-condensable component. And the heat transfer of droplet condensation is enhanced by the hydrophilic substrate rather than the hydrophobic substrate as expected, no matter adding the non-condensable component or not. In different conditions, the power law, which fits the droplet radius with time, is used to define the growth rate mathematically.

A new facility feasible for the investigation of dropwise condensation at a vertical polymer surface (9 × 6 mm, L × H) is described in detail. The droplets are liquefied out of humid air, which flows through a rectangular channel (12 × 32 mm, W × H) and passes the sub-cooled surface of a sensor. The latter one is flush mounted into one of the vertical channel walls beyond a hydrodynamic entry length of 550 mm determining perpendicular heat fluxes by measuring temperature differences. Furthermore the droplet covered surface is observed through the opposite channel wall by an infrared camera. The variable experimental parameters include temperature, water content and flow velocity of the humid air, as well as the surface temperature of the sensor. The scope of the experimental study is to investigate the mean heat transfer resistance of the condensate droplets which form on the substrate surface. The procedure is based on the determination of heat fluxes and the evaluation of the temperature differences between the substrate surface and the liquid/gas interface by means of thermography, both of them carried out synchronously. The experimental droplet heat transfer coefficient, h d , is evaluated as an average value and it considers both heat conduction through the droplets and the augmentation of heat transfer due to inner convection. The parameter variation covers Reynolds numbers between 7900 and 21400, relative humidities between 56% and 95% and air temperatures between 30 °C and 46 °C for a broad range of cooling temperatures. The latter one influences the droplet surface temperature and together with the water content of the bulk, it determines the driving force for mass transfer. h d was found to increase with the Reynolds number and the driving force for mass transfer. However, increasing the latter one beyond a certain value causes massive accumulation of noncondensable gases at the liquid/gas interface inhibiting the vapour mass flux and leading to invariant droplet heat transfer coefficients. The experimental data is correlated providing the basis for the experimental investigation of the heat transfer at the liquid/gas interface which will be done in future.

The present paper, convective dropwise condensation flow over a cold spot is numerically investigated using a 2D hybrid thermal lattice Boltzmann (LB) model with vapor-liquid phase change. After validating the present LB model, dropwise condensation on a cold spot as the nucleation region is simulated so as to study the nucleation and growth of the isolated droplet. The well-known power law for the growth of a single condensing droplet is demonstrated. And then, both simulations of dropwise condensation and convective dropwise condensation are carried out to study the effect of forced convective flow on dropwise condensation. Aiming to consider the effect of contact angle, the droplet is growing in the constant contact radius (CCR) mode. The results indicate that the forced convectional flow complicates the internal flow of the droplet and the vapor flow. The detouring flow (including the lee-side vortex) around the droplet in an isothermal system is replaced by the suction flow owing to condensation. The interaction between the dragging force of the vapor flow and the surface tension gradient changes the size of two symmetric vortices within the droplet in dropwise condensation. The size of these two vortices inside the droplet depends on the velocity and direction of convective flow. By comparison, the heat transfer enhancement of the superimposed flow is not worth mentioning in spite of different flow mode. Not affected by the vapor flow, the heat transfer is weakened by increasing of the contact angle owing to the change of conduction resistance. The present study illustrates the mechanisms of convective dropwise condensation flow in detail.

A single droplet model is developed to describe the droplet growth during dropwise condensation of moist air on a cold substrate. The condensation process is divided by the droplet surface into two parts. The first step, i.e. the processes of mass transfer from the surroundings to the droplet surface, is modeled by the Kinetic theory and the laws of continuum fluid dynamics formulated using the two-region concept (Knudsen layer and continuum region) at any droplet size and at any concentration of non-condensable gas (NCG). The second step, i.e. the heat transfer across the droplet, is governed by Fourier’s law of heat conduction. These three regions (the continuum region, the Knudsen layer and the region inside the droplet) are incorporated by the matching both the mass flow rates and the energy flow rates. From these, the droplet growth rate, the nucleation size of droplet, the temperature at the droplet surface and Knudsen layer interface can be evaluated depending on different conditions. For this, a numerical algorithm is developed to reflect the droplet dynamics sufficiently detailed, including nucleation, growth/coalescence, slide-off/fall-off, re-nucleation. This is applied to the simulation of the entire condensation process by putting the growth rate and minimum radius from single droplet model into the growth algorithm. Additionally, dropwise condensation experiments of moist air in different relative humidity (RH) are carried out for validation of the simulation results. Good agreement is obtained which demonstrates that the present droplet growth model for dropwise condensation of moist air is credible. The current model and experiments also indicate that the diffusion resistance of water vapor in air from the free stream toward the droplet surface has a significant influence for the heat transfer performance of dropwise condensation of moist air.

In modelling dropwise condensation, growth of the droplet is frequently assumed in an isolated form. However, for dropwise condensation of moist air the vapor diffusion from the surrounding to the droplet surface will be tremendously influenced by the blocking effect of the neighboring droplets. The influenced spatial distribution of water vapor totally determines a different condensation rate comparing with that by the isolated droplet model. In this work, a distributed point method (DPSM) as the methodof Green function is developed to capture the interaction effects of droplets without requiring solution of the diffusion equation and the numerical discretization. Due to its nature, the automaticallysatisfied boundary conditions make sure the solution accuracy based on the uniqueness theorem. The significant characteristics for the interaction effects between droplets are investigated by handling a series of droplet arrays. During dropwise condensation, a typical droplet array containing up to 1000 droplets is considered. The results indicate that the interaction effect between droplets is critical in accurately predicting the condensation behavior for dropwise condensation in the presence of non-condensable gas.

In this investigation dropwise-condensation heat transfer of out of a turbulent flow of humid air is experimentally investigated. The test section consists of a horizontal channel, sized 12 × 32 × 750 mm. The condensation takes placed on a 9 × 6 mm sized section of the vertical channel wall. A model based on the analogy of heat and mass transfer - previously used in the context of filmwise condensation - is adopted in order to describe the data obtained for varying bulk Reynolds numbers (3000–22000), temperatures (36∘C–55∘C) and relative humidities (36%–55%). Modifications are made in order to capture the effect of fog formation within the mixture and the enhancement of the area available for heat transfer induced by the droplets on the substrate. The formulation of the model is intended to be easily adoptable to other geometries, boundary conditions, types and orientations of the substrates. Previous investigations of this group were focused on the thermal resistance of the condensate. Based thereon, the present modelling completes the former approach, resulting in a model capable of predicting the total heat transfer coefficients of dropwise condensation from humid air. The predictions are validated using own experimental data as well as external data.

In this work, experimental and modeling investigations of convective dropwise condensation from moist air are carried out for the mechanistic understanding of the influence of non-condensable gas. For modeling, different droplet growth models in the presence of non-condensable gas are firstly developed by treating the droplet as an isolated form. During dropwise condensation, the presence of non-condensable gas brings some specific condensation characteristics, including the interaction effect between droplets and convection mass transfer. However, those characteristics cannot be reasonably captured by the droplet growth model. In this work, the distributed point sink method and the droplet Sherwood number are used to evaluate the inter-droplet interaction and convection mass transfer, respectively. Combining those progresses, the droplet growth rate is predicted and the prediction is evaluated by the measurements. Based on the accurate prediction for the droplet condensation rate, a semi-analytical modeling method is released to predict convective dropwise condensation of moist air. It considers the latent heat by condensation and the sensible heat by forced convection. Finally, this work presents the direct comparisons of the overall heat flux measured in experiments and the prediction. Furthermore, mechanistic understanding is discussed simultaneously and conclusively. Throughout this work, we highlight the reduction (the diffusion resistance of water vapor and the inter-droplet interaction) and enhancement (convection mass transfer) factors for dropwise condensation in the presence of non-condensable gas. In addition, in the case of this work, large droplets are more beneficial for heat transfer of dropwise condensation.

The enhancement mechanism of forced convective flow on dropwise condensation over a cold spot is numerically investigated by two-dimensional hybrid thermal lattice Boltzmann (LB) model based on the Shan-Chen pseudopotential LB model. After validating the present LB model, dropwise condensation over a cold spot as the nucleation region is simulated. The well-known power law for the growth of a single condensing droplet is demonstrated. Finally, the simulation of dropwise condensation considering the convection flow or not is carried out in the constant contact radius (CCR) mode. Using the CCR model, the effect of contact angle can be also investigated. The result of streamline field indicates that the forced convectional flow complicates the internal flow of droplet and main flow. The dragging force from main flow changes the size of two symmetric vortices inside the droplet. And the channel flow is also strongly influenced by the suction effect caused by condensation at the three phase contact line. By comparison, the heat transfer enhancement of the superimposed flow is not worth mentioning. The present study illustrates the mechanisms of dropwise condensation under forced convectional flow.