Maximum Droplet Radius Research Articles

Uniform and Persistent Jumping Detachment of Condensed Nanodroplets.

Realizing jumping detachment of condensed droplets from solid surfaces at the smallest sizes possible is vital for applications such as antifogging/frosting and heat transfer. For instance, if droplets uniformly jump at sizes smaller than visible light wavelengths of 400-720 nm, antifogging issues could be resolved. In comparison, the smallest droplets experimentally observed so far to jump uniformly were around 16 μm in radius. Here, we show molecular dynamics (MD) simulations of persistent droplet jumping with a uniform radius down to only 3.6 nm on superhydrophobic thin-walled lattice (TWL) nanostructures integrated with superhydrophilic nanospots. The size cutoff is attributed to the preferential cross-lattice coalescence of island droplets. As an application, the MD results exhibit a 10× boost in the heat transfer coefficient (HTC), showing a -1 scaling law with the maximum droplet radius. We provide phase diagrams for jumping and wetting behaviors to guide the design of lattice structures with advanced antidew performance.

Influence of inner wall roughness of supersonic separator on non-equilibrium condensation of CO2 benefiting flue gas decarbonization

Supersonic separators are energy efficient and environmental separation device. Recent work has demonstrated the potential of supersonic separators to separate CO2 from flue gas. Because the supersonic flows in the separator is accompanied by shock waves and non-equilibrium condensation, the current cognition level on flow behavior in the separator is low. This work establishes a numerical model to describe the high-speed two-phase flows in the separator and the non-equilibrium condensation of CO2 during carbon capture process, and clarify the influence of inner wall roughness on carbon capture process. The results show that the rapid expansion of gas pushes the thermodynamic system to non-equilibrium state and promotes the spontaneous condensation of CO2. Wall roughness has obvious influence on normal shock wave position, non-equilibrium condensation and normal shock wave intensity. When the roughness height increases by 0.1 mm, the maximum droplet radius in the separator decreases by 17.4%, liquid CO2 fraction decreases by 49.1%, and radial range of liquid phase decreases by 46.3%.

Theoretical investigation on microstructured hybrid surface heat transfer characteristics with Marangoni convection effect

The vapor condenses on the surface as a liquid film or distinct droplets, depending on the surface and fluid properties and the environmental conditions. The maximum droplet radius, micro-structure geometry, and Marangoni convection have proved to have a significant impact on the heat transfer characteristics. This paper investigates and compares the effects of different parameters on the heat transfer characteristics of three distinct hybrid surface models. The Marangoni convention effects originating from the temperature gradient are considered in all calculations. The results showed that an optimum maximum droplet radius exists in all three models in which the maximum hybrid heat flux can be obtained. The maximum hybrid heat flux is 133.94 (kW/m2) for the smooth model, 102.34 (kW/m2) for the Wenzel model, and 93.05 (kW/m2) for the Cassie-Baxter model. The results indicated that shorter micropillar heights result in higher complete dropwise and hybrid heat fluxes in the Cassie-Baxter and Wenzel models. The increase in the solid fraction is observed to increase the complete dropwise and hybrid heat fluxes as well.

Condensation Heat Transfer Correlation for Micro/Nanostructure Properties of Surfaces.

Condensation, which can be observed in nature as a phase change heat transfer phenomenon, is a critical phenomenon in industrial fields such as power generation, water desalination, and environmental control. Many existing studies have applied surfaces with different wettability by controlling the surface topology to enhance condensation heat transfer. However, the industrial applicability is close to zero due to the limited size and shape of surfaces and low supersaturation conditions. Here, we regulate the surface topology of large-area copper tubes, which are representative industrial metals. We fabricated four copper tubes with different surface structures. We analyzed the condensation phenomenon of the modified tube under specific supersaturation conditions by measuring the overall heat transfer coefficient. We analyzed the condensation phenomenon by measuring the condensation heat transfer coefficient. We have recognized that there is a difference between the maximum droplet radius and the droplet detaching frequency depending on the size and shape of the structure. We measured the contact angle and contact angle hysteresis to accurately analyze the droplet behavior on each surface. As a result, we show that there is a correlation between contact angle hysteresis (CAH) and the total heat transfer coefficient, indicating heat transfer performance. These findings can be applied when evaluating surfaces with excellent condensation heat transfer performance for use in real industrial environments, which can dramatically reduce time and cost.

Theoretical analysis on condensation heat transfer on the hydrophobic–hydrophilic hybrid surfaces with the impact of the Marangoni convection

Condensation occurs in the forms of filmwise condensation and dropwise condensation. Over the past decade, hybrid hydrophobic–hydrophilic surfaces have received significant attention due to their potential to enhance the heat transfer rate compared to complete dropwise condensation. The maximum condensed droplet radius in the hydrophobic region has a considerable impact on the heat transfer characteristics. This paper discusses the effect of the maximum droplet radius on hybrid surface heat transfer characteristics. On top of that, Marangoni convection effects originated due to the temperature gradient as a heat transfer resistance on the heat transfer rate is considered, modelled and investigated. Three models were investigated in this paper. The results indicate that there is an optimum maximum droplet radius for each model that can improve the heat transfer rate. When the filmwise region width increases from 0.5 mm to 1.0 mm, the optimum maximum droplet radius increases from 0.25 mm to 0.3 mm. For a fixated droplet contact angle and filmwise and dropwise region widths, the hybrid heat flux of the smooth dropwise model can be up to 1.55 times higher than that of the Cassie–Baxter model, and the hybrid heat flux of the smooth dropwise model can be up to 1.38 time higher than that of the Wenzel state. Finally, considering Marangoni convection showed up to a 30% increase in the heat transfer coefficient in some cases.

Investigation of the effect of maximum droplet radius on condensation heat transfer on hydrophobic-hydrophilic hybrid surfaces with the effect of Marangoni convection

Condensation occurs in two modes, including filmwise and dropwise condensation. On a hybrid surface, the maximum radius of the condensed droplet on the surface in the dropwise region significantly affects the rate of heat transfer. In this paper, the effect of maximum droplet radius on heat transfer on hybrid surfaces is investigated. In this paper, the effect of Marangoni convection-current due to the temperature gradient- is considered as a resistance in the heat transfer process. The results indicate that an optimum value of the maximum droplet radius exists to enhance the condensation heat transfer of steam in the hybrid surface that is dependent on the surface subcooling degree, filmwise region width and the contact angle. As the surface subcooling degree increases from 1.0 K to 10 K, the optimum maximum radius of the droplet in the dropwise region increases from about 0.25 mm to 0.3 mm. Also, the optimum maximum radius of the droplet increases from about 0.25 mm to 0.35 mm when the filmwise region width is increased from 0.5 mm to 1.0 mm. Finally, the results of applying the effect of Marangoni convection indicate a 30% increase in the heat transfer coefficient in the case of applying Marangoni convection.

CONCEPTUALIZATION, THERMAL ANALYSIS, AND MANUFACTURING OF NANO-TEXTURED MICRO-STRUCTURED SURFACES FOR ENHANCED CONDENSATION HEAT TRANSFER

In the present study, nano-micro-structured surfaces have been systematically designed and manufactured in order to generate controlled dropwise condensation mode for enhanced heat transfer during phase-change from vapor to liquid. The conceptualization of micro-structures was conducted by using thermal modelling of an individ-ual droplet pinned at a single micro-hexagonal cavity. By varying droplet radius, resulting contact angles and geo-metric dimensions of micro-structure, threshold values have been determined for the later manufacturing process. According to the calculations for instance at contact angles of 150°, a subcooling of 1 K and a maximum droplet radius of 100 µm, the edge length and the depth of the micro-structures should be kept below 50 µm and 25 µm, respectively. Ensuring these parameters, a roughly 100 % larger heat transfer coefficient would result compared to that predicted by the classical Nusselt theory for filmwise condensation. Taking into account the mathematical analysis, laser ablation technique was adopted on 7075 aluminum samples to emboss hexagonal structures with respect to the predicted dimensions. After this step, the samples were electrochemically etched in order to achieve contact angles of more than 150° to ensure superhydrophobic solid-liquid interaction at the surface. Measurements with a high-precision microscope show that most of the structure dimensions and geometric shape were precisely manufactured. The Tensiometer results disclosed that the surface topography at all samples exhibit contact angles larger than 150° for a sessile droplet with a radius of 100 µm pinned on an individual micro-hexagon.

Supersonic refrigeration performances of nozzles and phase transition characteristics of wet natural gas considering shock wave effects

Laval nozzle is the critical part of supersonic separator to provide refrigeration environment. Due to the back pressure at the outlet of supersonic separator in dehydration process, the condensation characteristics of water vapor and the refrigeration performances of the nozzles are affected by the shock wave. Herein, mathematical models for the supersonic condensation and flow of the methane-water two-phase flow model were established, which were verified by the experimental data. The effects of different divergent angles on the refrigeration and condensation behavior in the Laval nozzle were studied considering shock wave. The results show that the refrigeration performance of the nozzle will be worsen under the presence of shock waves. With the divergent angle of the nozzle increased from 2° to 8°, the lowest temperature was decreased from 304.4 K to 291.8 K, the liquid mass fraction at the nozzle outlet was decreased from 0.84% to 0.133%, the maximum droplet radius that can be obtained was reduced from 2.54 × 10−7 m to 1.69 × 10−7 m due to the forward movements of the shock waves. The divergent angle of the nozzle is recommended to be designed to 4°–6° in consideration of the refrigeration performance.

Heat transfer calculation under film and drop condensation on tube with heat intensifiers

This article discusses well-known models and equations for calculating the heat transfer gain during film and drop condensation on a pipe, which need to be improved. Film condensation heat transfer on horizontal pipe made from brass with knurling is analyzed. The heat transfer data for investigated steam mixture condensation on horizontal tube with spikes heat intensifiers is analyzed. It is noted that the functions of drop growth for various conditions and their distribution must be known for calculating heat transfer during drop condensation. The maximum droplet radius, droplet size distribution, and then condensation heat transfer performance could be adjusted with special condensing surfaces, such as gradient, superhydrophobic, grooved, hydrophobic-hydrophilic patterned and hybrid surfaces. Now the nanoscale structures can by nanotechnologies.

Prediction of supersonic condensation process of methane gas considering real gas effects

To clarify the condensation characteristics of natural gas under a high pressure and obtain accurate nucleation parameters, traditional Internal Consistent Classical Nucleation Theory (ICCT) model for single-component gas was improved. A mathematical model for the supersonic condensation flow of methane gas was established based on the improved ICCT model, and the supersonic condensation process was experimentally verified. The field characteristics of condensation flow and isentropic flow were compared, and the low-temperature liquefaction characteristics of methane gas in the Laval nozzle were studied. The results show that the calculation results of improved model considering the real gas effect are more accurate than the results of original ICCT model. When methane gas is condensed, a weak condensation shock wave propagates in the nozzle; compared with the isentropic expansion process, the pressure and temperature at nozzle outlet increase. In a very short distance, the nucleation rate of methane gas sharply increased from 0 to a maximum value of 4.834 × 1021 m−3 s−1 (approximately at x = 0.367 m). The maximum droplet radius, droplet number, and liquid mass fraction are 2.112 × 10−7 m, 4.128 × 1014 kg−1, and 5.437%, respectively.

An efficient method for removing hydrogen sulfide from natural gas using supersonic Laval nozzle

A new method was proposed for hydrogen sulfide removal from natural gas through the utilization of supersonic flow in a Laval nozzle. For this purpose, a mathematical model was established for the supersonic non-equilibrium condensation flow of the binary methane-hydrogen sulfide mixture. The condensation parameters were numerically calculated and described in detail, and a sensitivity analysis was carried out to investigate the influence of the inlet parameters on the supersonic condensation flow. The results show that when the inlet temperature and pressure were 290K and 5MPa respectively, and the mole fraction of hydrogen sulfide was 15%, the removal efficiency of hydrogen sulfide was 64.83%, which indicates that the use of supersonic separation technology for this application is indeed feasible. It was also found that with the decrease of inlet temperature or the increase of inlet pressure, the nucleation site moved forward (i.e. closer to the throat), and the maximum droplet radius and liquid mass fraction of hydrogen sulfide increased. When the mole fraction of hydrogen sulfide was less than 5%, however, the liquid mass fraction of hydrogen sulfide was almost zero. Therefore, it appears that using a reasonable hydrogen sulfide fraction, a lower inlet temperature, and a higher inlet pressure can promote the supersonic condensation of hydrogen sulfide in the Laval nozzle and improve the efficiency of the removal process. These results suggest that supersonic separation technology can provide an efficient and environment-friendly way to remove hydrogen sulfide from natural gas, thereby reducing emissions.

Mode selection between sliding and rolling for droplet on inclined surface: Effect of surface wettability

Onset of droplet motion is important for various applications, including dropwise condensation and water management in fuel cells. In order to determine critical conditions for onset of motion and specific motion mode, a general problem having a droplet sheared by a gas stream on inclined surface is investigated. Two criterion equations are theoretically established for onset of droplet sliding and rolling independently, including dimensionless parameters of Bond number (Bn), Ohnesorge number (Oh) and Weber number (We), inclination angle parameter and wettability parameters. The criterion equations predict critical gas velocity, maximum droplet radius, and “sliding angle” or “rolling angle”. Droplet sliding predictions agree well with experimental data in the literature. Criterion surfaces of sliding or rolling are constructed to verify if sliding or rolling can be initiated, influenced by both equilibrium contact angle and contact angle hysteresis. By coupling the criterion equations of sliding and rolling, we develop a mode selection criterion equation, which is only dependent on equilibrium contact angle θe. Three regions are clarified: (1) for 126.3° < θe < 147.0°, a droplet rolls if Bn < Bnt and slides if Bn > Bnt, where Bnt is the transition Bond number; (2) for θe < 126.3°, a droplet only slides; (3) for θe > 147.0°, a droplet only rolls. The theoretically determined 147.0° contact angle is newly recommended as the contact angle boundary between hydrophobicity and super-hydrophobicity. One of the applications of this work is to provide a general guideline for droplet detachment or retention in fuel cells and condensers.

CFD-based shape optimization of steam turbine blade cascade in transonic two phase flows

In this study CFD-based shape optimization of a 3D nozzle and a 2D turbine blade cascade is undertaken in the presence of non-equilibrium condensation within the considered flow channels. A two-fluid formulation is used for the simulation of unsteady, turbulent, supersonic and compressible flow of wet steam accounting for relevant phase interaction between nucleated liquid droplets and continuous vapor phase. An in-house CFD code is developed to solve the governing equations of the two phase flow and was validated against available experimental data. Optimization is carried out in respect to various objective functions. It is shown that nucleation rate and maximum droplet radius are the best suited target functions for reducing thermodynamic and aerodynamic losses caused by the spontaneous nucleation. The maximum increase of 2.1% in turbine blade efficiency is achieved through shape optimization process.

Experimental investigation on steam condensation heat transfer enhancement with vertically patterned hydrophobic–hydrophilic hybrid surfaces

The maximum droplet radius and droplet size distribution are significant for dropwise condensation heat transfer. Adjusting the maximum droplet radius and droplet size distribution with vertically patterned hydrophobic–hydrophilic hybrid surface is an effective method to enhance and optimize condensation heat transfer performance. The maximum droplet radius and droplet size distribution adjustment with hydrophobic–hydrophilic hybrid surface, and the resultant heat transfer performance are investigated experimentally in this paper. The results indicate that with the increase of hydrophobic region width, the maximum droplet radius on hydrophobic region increases while the droplet population density decreases. An optimum hydrophobic region width exists and the steam condensation heat transfer performance decreases with the increase of hydrophilic region width. And the performance can be larger than that of complete dropwise condensation for appropriate hybrid surfaces. The steam condensation heat transfer performance on the optimum hybrid surface is about 23% higher than that of complete dropwise condensation at surface subcooling of 2.0K. Steam condensation heat transfer enhancement factor increases with the increase of hydrophobic region width first and then decreases with its further increase. The optimum hydrophobic region width is about 0.55mm and the corresponding optimum maximum droplet radius is about 0.25mm. Heat transfer enhancement factor decreases with the increase of surface subcooling and the optimum heat transfer enhancement factor is also significantly dependent on the surface subcooling. When the surface subcoolings are 2.0K, 4.0K and 6.0K, the optimum heat transfer enhancement factors are about 1.23, 1.11 and 1.07, respectively. Steam condensation heat transfer can be enhanced with hydrophobic–hydrophilic hybrid surface more effectively at low surface subcooling. The experimental results and theoretical analysis agrees well to each other.

Analysis of condensation heat transfer enhancement with dropwise-filmwise hybrid surface: Droplet sizes effect

The maximum droplet radius during dropwise condensation can significantly influence the heat transfer characteristics. On the dropwise-filmwise hybrid surface, droplets on the dropwise region can remove through filmwise region spontaneously driven by the surface free energy difference between the dropwise and filmwise regions, and thus the maximum droplet radius (equivalent to the departure radius for the complete dropwise condensation) can be adjusted by the configurations of hybrid surface. The condensation heat transfer enhancement of steam with hybrid surface is investigated in this paper by integrating the dropwise and filmwise condensation heat transfer models. The influence of maximum droplet radius on heat flux of dropwise region, the liquid film thickness and heat flux of filmwise region are investigated, respectively. Accordingly, the heat transfer contributions of two regions to the heat transfer characteristics of hybrid surface are analyzed. Finally, the influences of surface subcooling degree, contact angle and contact angle hysteresis on heat transfer characteristics of hybrid surface are discussed. The results indicate that an optimum value of the maximum droplet radius exists to enhance the condensation heat transfer of steam with the hybrid surface, which is dependent on surface subcooling degree, filmwise region width and contact angle while independent on contact angle hysteresis. With the surface subcooling degree increases ranging from 1.0K to 10K, the optimum maximum radius of droplet on dropwise region increases from about 0.2mm to 0.375mm. The optimum maximum radius of droplet increases from about 0.25mm to 0.5mm when the filmwise region width increases from 0.5mm to 1.0mm. The optimum maximum radius of droplet decreases with the increase of the contact angle. Therefore, steam condensation heat transfer performance can be regulated and optimized by designing the hybrid surface appropriately. The results also indicate that heat transfer enhancement factor for the hybrid surface is larger than 1.0 for the low surface subcooling or the condensing surface with small contact angle or large contact angle hysteresis. Therefore, the hybrid surface can effectively enhance the condensation heat transfer for the special cases, such as those with low surface subcooling degree, or with small contact angle and large contact angle hysteresis. For the case discussed in this paper, the maximum enhancement factor can approach up to about 1.18.

Identification of the level of downdraft formation during severe thunderstorms: a frequency domain analysis

A study aimed at identifying the level of pressure at which cloud droplets break up or split, leading to downdraft formation, during severe thunderstorms of the pre-monsoon season (April–May) over Kolkata (22°32′, 88°20′) was carried out. To this end, frequency domain analyses were used to compute Fourier line spectra. The parameters maximum droplet radius and the upward velocity were considered to be the entries to the time-series analysis. The results obtained using this spectral approach, which represent a component of the frequency-domain time-series analyses, were quantitatively validated utilizing probabilistic and Taylor series considerations. The results reveal that 700 hPa is the critical level for the initiation of the splitting of the cloud droplets and, consequently, the downdraft during severe thunderstorms of pre-monsoon season over Kolkata. However, the results also indicate that during severe thunderstorms accompanied by hail, the downdraft level may occur at a lower pressure level or higher altitude.

Primary ice nucleation in orographic cirrus clouds: A numerical simulation of the microphysics

AbstractIce particle production by the processes of homogeneous freezing and heterogeneous nucleation in orographic cirrus clouds is studied using a simple adiabatic ascending‐air‐parcel model. Homogeneous freezing rates in the model are based on a formulation by Jeffery and Austin, which matches with observed rates, modified according to the solution effect. Two alternative ice nuclei (IN) activation spectra are applied, one dependent upon temperature and the other upon ice supersaturation. Simulations are performed for air parcels with initial dew‐point temperatures, Td, in the range from −20 to −45°C and constant vertical velocities, w, of 0.1 to 5.0 m s‐1. In modelled clouds with Td ⩾ 30°C, heterogeneous nucleation initiated by IN is found to dominate ice formation, since homogeneous freezing rates are so low. In modelled clouds with Td ⩽ −35°C, pure liquidwater homogeneous freezing rates are large, but inclusion of sufficient quantities of IN may completely suppress aqueous solution droplet growth, dilution and homogeneous freezing, with heterogeneous nucleation then remaining dominant even at very low temperatures. the IN number concentrations required for homogeneous freezing suppression, for a fixed cloud condensation nucleus (CCN) activation spectrum, are found to increase with increasing w‐heterogeneous nucleation at low temperatures is therefore much more viable at the low w values found in non‐orographic compared with orographic cirrus clouds. the common conception of a deficit of IN aloft is challenged, and, because of the apparent sensitivity of cirrus cloud microphysical and radiative properties to these aerosol particles, IN measurements at cirrus levels, in addition to CCN measurements, are suggested as vital. the model results suggest that it may be possible to interpret measurements of peak liquid‐water content, or possibly maximum droplet radius, in orographic cirrus clouds in terms of the dominant ice nucleation mode.