No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Numerical simulation of bubble condensation using CF-VOF
... This ensures that the total volume of the cell is occupied by either vapor, liquid, or liquid-vapor phases. The interface between liquid and vapor phases can be tracked by solving the following transport equation for the vapor phase in the Volume of Fluid (VOF) method [31,32]: ...
... where S h is the volumetric energy source and E is the sensible enthalpy [31,32]: ...
... Here, T is the temperature of the fluid and C p is the specific heat capacity, which can be calculated from the following equation [31,32]: ...
This study represents the development and optimization of a micro-baffle design to enhance heat transfer in film boiling. Numerical simulations are performed using an open-source computational fluid dynamics (CFD) model, which incorporates the Lee model for momentum source associated with the phase change, and the Volume of Fluid (VOF) method to capture bubble dynamics. A comparison of the numerical results with the previous numerical and experimental data confirmed the validity of the numerical model. The influence of key design parameters was systematically investigated. The results revealed that a vertical baffle provided the maximum performance. The optimal baffle design achieved a 57.4% improvement in the Nusselt number and a 66.4% increase in critical heat flux (CHF). Furthermore, the proposed design facilitated continuous bubble formation, even with a reduced temperature difference between the heated surface and the subcooled liquid, which is crucial for energy-efficient thermal management in engineering systems. Ultimately, this study demonstrates the potential of micro-baffle designs in controlling bubble dynamics and improving heat transfer in film boiling, thereby aiding the design of efficient thermal systems.
... The second challenge lies in the phase change models. The phase change and heat transfer models for traditional Eulerian methods have been relatively well-developed, 10,24-27 e.g., Samkhaniani and Ansari 25 simulated the condensation process of single and multiple vapor bubbles using the Tanasawa mass transfer model through the CF-VOF method and found that the results are significantly relevant to the mass transfer coefficient. However, research on gas-liquid phase change models for mesh-free particle methods started later, and still requires more studies, and the source term of velocity divergence used in Eulerian methods is not very suitable for particle methods. 1 There has been more research on boiling models for particle methods than on condensation models. ...
... The 1D Stefan problem was originally introduced to validate solidification simulation, 57 and it has since become a widely employed benchmark for boiling simulation. 10,25,26,58 Therefore, it is used to validate the accuracy of the present boiling model in this study. As shown in Fig. 13, the sketch of the Stefan problem depicts an initial state Physics of Fluids ARTICLE pubs.aip.org/aip/pof ...
... The curves are not as linear as Fig. 23, of which the main reason is that the initial bubble diameter is larger and the bubble shape cannot remain spherical during condensation but ellipse. 25 The numerical results of bubble lifetimes are compared with other numerical and experimental results, as shown in Fig. 27(b). The results of the proposed BC-MPS-SPH method generally agree with the experimental data. ...
The description of boiling and condensation phenomena presents a challenging problem. We propose a Lagrangian incompressible–compressible mesh-free particle method for modeling multiphase flows involving boiling and condensation. This multiphase scheme combines the moving particle semi-implicit method with the smoothed particle hydrodynamics method, while incorporating a phase transformation model based on heat transfer to simulate gas–liquid phase transformation. Gas volume expansion and shrinkage are accounted for through particle splitting and merging techniques. Numerical investigations demonstrate the effectiveness and accuracy of this multiphase method and phase transformation model, including simulations of multiphase dam-break flow, rising bubble, Stefan problem, and sucking problem. Our approach successfully simulates the boiling growth and condensing collapse of vapor bubbles, which is validated against numerical and experimental results. Stable and relatively accurate simulations can be achieved for bubble collapse processes under different water subcooling degrees, gas overheating degrees, surface tension values, and bubble sizes. The complex process of boiling before condensation can be accurately reproduced.
... Figure 2 shows that the numerical model is in excellent agreement with the analytical solution for interface position against time, for all three values of vapour thermal conductivity tested. The model is also tested against the Stefan problem presented by Samkhaniani and Ansari [5], where the condensation of a planar liquid film is simulated and compared to the analytical solution of Welch and Wilson [6]. The same mesh is used as in the evaporating Stefan case, where in this case the first ten cells are filled with saturated liquid, and the remainder of the domain is filled with vapour subcooled by Δ (/0 = 10 . ...
... The isothermal wall on the liquid side is at the saturation temperature ()* of 380.26 K, while the vapour side is at the subcooled vapour temperature. Fluid properties used are those of saturated water at ()* = 0.130 MPa and are described by Samkhaniani and Ansari [5]. ...
... The liquid superheat, Δ , is 5K. The radius of the bubble in time is described analytically by the solution of Scriven for the heatcontrolled growth of a spherical bubble [7] 5 , and is the Jakob number. The initial temperature distribution is described by ...
A methodology for the modelling of phase change phenomena in two-phase flow is presented, based on interface capturing simulation and the mechanistic modelling of interfacial heat and mass transfer. The volume of fluid approach is adopted, utilising a compressive scheme to maintain interface sharpness, allowing a continuum representation of mass and heat source terms to be used. The methodology is verified against analytical solutions for both evaporation and condensation phase change problems, demonstrating excellent agreement even in the case of a large phase density ratio and high rate of evaporation.
... The constant γ is taken to be equal to 1 for the flow boiling as recommended by Marek and Straub [34], Samkhaniani and Ansari [31,35], Silvi et al. [30], and Kushwaha and Kumar [36]. The compressive velocity U → C can be calculated with the equation (15), where the value of C α is taken equal to 1 based on previous studies by Samkhaniani and Ansari [21,31,35]: ...
... The constant γ is taken to be equal to 1 for the flow boiling as recommended by Marek and Straub [34], Samkhaniani and Ansari [31,35], Silvi et al. [30], and Kushwaha and Kumar [36]. The compressive velocity U → C can be calculated with the equation (15), where the value of C α is taken equal to 1 based on previous studies by Samkhaniani and Ansari [21,31,35]: ...
... To suppress any smearing of the interface, the value should not be kept as zero and a finite value is recommended between 1 to 4 [48]. In present case, compression coefficient value of 1 is used as it has been used in previous studies [21,31,35,49]. With value greater than 1, enhanced compression of the interface can be achieved. ...
... These two benchmark cases are presented and solved in Sections 3.1 and 3.2. The analytical solutions [48] for the temperature distribution (T(x, t)) and the thickness of vapor film (δ) are as follows ...
... The analytical solution [48] to calculate the liquid film thickness (δ an (t)) is given as ...
... • The temperature profile across the film is linear, • Effects of forces caused by inertia and interface shearing stress are neglected. Based on the aforementioned assumptions, the analytical solution [48] for the liquid film thickness (δ) is ...
Simulations of thermally driven phase change phenomena of nanofluids are still in their infancy. Locating the gas-liquid interface location as precisely as possible is one of the primary problems in simulating such flows. The VOF method is the most applied interface description method in commercial and open-source CFD software to simulate nanofluids' thermal phase change. Using the VOF method directs to inaccurate curvature calculation, which drives artificial flows (numerical non-physical velocities), especially in the vicinity of the gas-liquid interface. To recover accuracy in simulation results by VOF, a solver coupling VOF with the level-set interface description method can be used, in which the VOF is employed to capture the interface since it is a mass conserving method and the level-set is employed to calculate the curvature and physical quantities near the interface. We implemented the aforementioned coupled level-set and VOF (CLSVOF) method within the open-source OpenFOAM® framework and conducted a comparative analysis between CLSVOF and VOF (the default interface capturing method) to demonstrate the CLSVOF method's advantages and disadvantages in various phase change scenarios. Using experimental mathematical correlations from the literature, we consider the effect of nanoparticles on the base fluid. Results shows that the new inferred technique provides more precise curvature calculation and greater agreement between simulated and analytical/benchmark solutions, but at the expense of processing time.
... The γ = 0.1 − 1 is suggested for dynamically renewing water surfaces such as jets and moving films and γ < 0.1 for stagnant surfaces [27]. Samkhaniani and Ansari [28] report that the bubble lifetime is highly sensitive to the choice of γ in vapor condensation simulations and suggest that an appropriate value must be selected for simulations in comparison with experiments. ...
... The strength of the parasitic current is often measured with the maximal magnitude of velocity |u| for a single bubble placed in a stagnant liquid in zero gravity in the absence of phase change. The current may distort the interface [31] or impair the mass transfer estimation during phase change [28], rendering nonphysical results. Thus, it is crucial to improve surface tension modeling to avoid the parasitic current. ...
... The rising of a single vapor bubble is simulated similar to [28,43]. The bubble is introduced at the saturated temperature T sat = 380.2 ...
Pure numerical simulation of phase-change phenomena such as boiling and condensation is challenging, as there is no universal model to calculate the transferred mass in all configurations. Among the existing models, the sharp interface model (Fourier model) seems to be a promising solution. In this study, we investigate the limitation of this model via a comparison of the numerical results with the analytical solution and experimental data. Our study confirms the great importance of the initial thermal boundary layer prescription for a simulation of single bubble condensation. Additionally, we derive a semi-analytical correlation based on energy conservation to estimate the condensing bubble lifetime. This correlation declares that the initial diameter, subcooled temperature, and vapor thermophysical properties determine how long a bubble lasts. The simulations are carried out within the OpenFOAM framework using the VoF method to capture the interface between phases. Our investigation demonstrates that calculation of the curvature of interface with the Contour-Based Reconstruction (CBR) method can suppress the parasitic current up to one order.
... Numerical simulations of subcooled boiling flow can be found in the literature, using either the VOF-CSF approach based on the open source software OpenFOAM [64,76,77] , a modified user defined function (UDF) in the ANSYS-FLUENT CFD software [78][79][80] and a geometric reconstruction of piecewise linear interface calculation (PLIC) based VOF method [81] . In particular, Jeon et al. [78] estimated the rate of bubble condensation in terms of the heat transfer coefficient at the interface obtained from the bubble velocity, liquid subcooled temperature and transient condensing spherical-bubble diameter. ...
... Due to the velocity gradients, the condensing vapor bubble moves towards the region of higher velocity and then back to lower velocity region according the rate of subcooling. Samkhaniani and Ansari [77] accounted for the effect of (i) constant saturation temperature and (ii) local saturation temperature of the vapor bubble as a function of thermodynamic pressure which is non-uniform in quiescent subcooled water due to surface tension and acceleration due to gravity. These authors observed that for constant saturated temperature of the bubble, the bubble diameter reduces linearly due to the uniform temperature difference between the saturated vapor bubble and the subcooled liquid phase. ...
... From these results it is observed that the condensation of the static bubble is significantly affected by the grid resolution; in particular, the condensation rate is over-predicted by a coarse grid with insufficient resolution. The ratio of surface area to condensing bubble volume, a b / v b is higher for a small bubble, leading to very fast condensation when the bubble diameter becomes close to two or three grid sizes, h [77] . Therefore, the bubble radius reduces faster when using the coarser grid. ...
... For the case of condensation of FC-72 in vertical downflow in a tube, Lee et al. [8] presented a value of r = 10 4 s −1 as the most appropriate value for the condensing configuration, working fluid, and operating conditions of their study. Samkhaniani and Ansari [9] studied bubble condensation using the CF-VOF method with the Tanasawa model [10] for interfacial mass transfer. This highly accurate model requires the presence of a liquid/vapor interface, so it cannot be used for boiling and subcooled flows in general. ...
... This highly accurate model requires the presence of a liquid/vapor interface, so it cannot be used for boiling and subcooled flows in general. In the numerical part of the paper by Samkhaniani and Ansari [9], the instantaneous bubble diameter was compared with the experimental data from the same study, showing good agreement, even when the bubble shape changes from circular to elliptical under the effect of fluid pressure. ...
This paper presents simulations based on the VOF method under the OpenFOAM package for a rising/condensation bubble in a vertical channel and subcooled boiling flow in a horizontal serpentine tube, with Lee’s model to account for phase change phenomena. The main objective of this study was to test the OpenFOAM solver icoReactingMultiphaseInterFoam for condensation and evaporation phenomena using Lee’s model. In addition, conjugate heat transfer, largely neglected by the OpenFOAM community, was considered in the second configuration of interest by adopting the modeling approach of the baffle3Dregion library and implementing it in the solver to examine its reliability for phase-change flow situations. With an average relative error of 13.4%, the numerical heat transfer coefficient for the rising/condensation bubble showed good agreement with the Ranz and Marshall correlation, which is widely used in the Eulerian-Eulerian simulations. For the second configuration, the time-averaged outlet volume fraction results of the test case 2 and 3 showed good agreement with numerical study of the literature (Yang et al., 2008.), with mean relative errors of 1.9% and 11.2%, respectively. However, for Case 1, the relative difference was higher, reaching a value of 34%, probably due to the difference in mesh size between the two studies at the tube outlet. Additionally, similar flow patterns were observed for all test cases.
... The present solver was developed in OpenFOAM and is based on interFoam. However, the standard interFoam solver can cause unphysical spurious currents at the interface especially for low Capillary numbers (Georgoulas et al., 2015;Samkhaniani and Ansari, 2016;Guillaument et al., 2015;Gueyffier et al., 1999;Renardy and Renardy, 2002;Deshpande et al., 2012), which will also lead to unphysical fluctuations in the pressure field. Hence, in the first step, a VOF smoothing method was implemented to limit these spurious currents. ...
... In OpenFOAM, the two-phase flow solver, interFoam, suffers from non-physical spurious currents (Georgoulas et al., 2015;Samkhaniani and Ansari, 2016;Guillaument et al., 2015;Gueyffier et al., 1999;Renardy and Renardy, 2002;Deshpande et al., 2012), which are generated due to sharp changes of the volume fraction over a thin region at the interface . In this work, spurious currents were suppressed by using Hoang's treatment (Hoang et al., 2013). ...
Due to the dominance of interfacial forces, microreactors are commonly applied to multiphase processes where control over the dispersed phase volume is critical. For the design of such microfluidic devices, it is therefore important to accurately predict droplet breakup and the resulting two-phase flow pattern using computational tools. In this work, we show that integrating a dynamic contact angle model into a volume-of-fluid (VOF) solver significantly increases the prediction accuracy of droplet formation in a microfluidic T-junction compared to earlier studies with a constant contact angle model. Furthermore, it was found that the droplet formation is more sensitive to the chosen value of the advancing contact angle, while the receding contact angle showed only a minor influence. The present findings confirm that using a dynamic contact angle model with a VOF approach to simulate droplet formation in microchannels will provide more accurate predictions.
... The understanding of the fluid mechanics during the heat and mass transfer process plays a significant role in the design and optimization of these industrial applications. Among others, the bubble condensation, which includes the complex coupling of strong turbulence , bubble dynamics , and heat and mass transfer across the interface (Samkhaniani and Ansari, 2016) deserves extensive research due to the lack of its understanding. Therefore, bubble condensation with further quantitative analysis should be conducted to allow the deployment of reliable tools. ...
... Based on the Schrage model, Tanasawa (1991) further simplified it by suggesting the dependence of mass flux on temperature jump between the interface and vapor phase. The application of the Schrage model and Tanasawa model in the study of phase change phenomena can be found in Zeng et al. (2015) and Samkhaniani and Ansari (2016). Overall, these two models are both physically based and account for the kinetic energy effects. ...
The vapor bubble condensation process is numerically investigated via three-dimensional (3D) simulation using Volume of Fluid method (VoF). Two phase change models, i.e. Lee model and Tanasawa model, are implemented and assessed with experimental data. Since no mesh-independent results can be obtained with the Lee model, the Tanasawa model is adopted for the study of bubble condensation process. The single vapor bubble condensation in subcooled quiescent water is analyzed. Different influencing factors on bubble condensation, i.e. diameter size, subcooling and liquid properties, are studied. With the increase of the bubble diameter, the condensation rate increases due to increase of the shear stress between the vapor bubble and the cold bulk, resulting in the turbulence inside the bubble being more intensive and the thermal field around the bubble more unstable. High subcooling increases the mass flux across the interface, which brings about the interface instability on the bubble surface and bubble breakup is observed. The increase of the liquid viscosity restricts the bubble rising and deformation, which reduces the convective heat transfer and condensation rate. The occurrence of bubble central breakup due to the decrease of surface tension enlarges the effective condensation area and increases the condensation rate.
... The authors employed the interfacial liquid layer and a coupling method between momentum and energy equations to evaluate the amount of heat transfer during the condensation process. Samkhaniani and Ansari (2016), by employing the CF-VOF method, showed that there is a relationship between bubble lifetimes and bubble size in a condensation process. It was shown that the former feature is approximately in proportion to the latter one. ...
... In fact, due to the size reduction, (for instance, the area ratio of the bubbles will be A1/A2 = 0.002, in which A1 is the area of the small bubble at t = 0.06 (s) (see Fig 8a) and A2 is the area of the original bubble), the numerical simulation shows a slight unsymmetrical behavior. This behaviour was also observed in the previously published numerical studies conducted by Jeon et al., 2011, Liou et al., 2015, Samkhaniani and Ansari 2016and Paramanantham et al., 2018. Interestingly, reducing the size of the initial bubble, as shown in Fig. 9, may postpone the coalescence of two bubbles in a similar condition or even prevent it to occur. ...
Numerical studies are performed to investigate the condensation behavior of single and multiple bubbles in subcooled boiling flow. An open-source code is developed to model the dynamic behavior of the bubbles in real-time. The Newtonian flow is considered and relative equations are solved employing a coupled Level Set (LS) and Volume of Fluid (VOF) method known as CLSVOF model according to the Pressure Implicit with Splitting of Operators (PISO) algorithm. Initially, the numerical findings were compared and verified by available experimental data. The result of a single bubble condensation revealed that the initial bubble size, the subcooling of liquid, and the velocity of the flow not only significantly affect the bubble deformation behavior, but also the rate of condensation. For multiple bubbles, the results revealed that due to interaction between bubbles, bubbles' dynamic condensation behavior is more complex compared to a single one. Due to this interaction, it is found that the rate of bubble condemnation and condensation process vary. Furthermore, the effects of the gradient velocity, gradient temperature, and gap between multiple bubbles on the rate of mass transfer through the condensation are studied. A critical gap between multiple bubbles is introduced. It is found that when (* = / ≥ 2) for different bubble diameters, the effect of bubbles interaction can be ignored. Here * is a dimensionless gap of center-to-center of bubbles.
... Due to the smeared nature of the interface, the curvature and the pressure jump across the interface obtained from the simulations do not match the theoretical value which generates spurious velocities (Deshpande et al., 2012). These spurious velocities introduce nonphysical flows near the interface which may cause the bubble to numerically drift as well as alter the heat/mass transfer coefficients in supersaturation and temperature driven phase change processes (Samkhaniani and Ansari, 2016;Saufi et al., 2019;Vachaparambil and Einarsrud, 2020). The works by Popinet (2018) and Deshpande et al. (2012) have reviewed the various approaches reported to mitigate these effects, namely: improved curvature estimation, force balance between surface tension and pressure gradient (for static cases), time step constraint when surface tension is calculated explicitly and temporally implicit approach to estimate surface tension. ...
... around 50-60 is typically used in thermal and supersaturation driven phase change processes (Samkhaniani and Ansari, 2016). Consequently, a sub-millimeter bubble, of radius equal to 0.25 mm, is initialized in a 1 mm 2 domain that is meshed by 120120 cells and the corresponding maximum time step, calculated (11), is set at 0.6 μs. ...
Amongst the multitude of approaches available in literature to reduce spurious velocities in Volume of Fluid approach, the Sharp Surface Force (SSF) model is increasingly being used due to its relative ease to implement. The SSF approach relies on a user-defined parameter, the sharpening coefficient, which determines the extent of the smeared nature of interface used to determine the surface tension force. In this paper, we use the SSF model implemented in OpenFOAM® to investigate the effect of this sharpening coefficient on spurious velocities and accuracy of dynamic, i.e., capillary rise, and static bubble simulations. Results show that increasing the sharpening coefficient generally reduces the spurious velocities in both static and dynamic cases. Although static millimeter sized bubbles were simulated with the whole range of sharpening coefficients, sub-millimeter sized bubbles show nonphysical behavior for values larger than 0.3. The accuracy of the capillary rise simulations has been observed to change non-linearly with the sharpening coefficient. This work illustrates the importance of using an optimized value of the sharpening coefficient with respect to spurious velocities and accuracy of the simulation.
... For α values falling between 0 and 1, the grid cell is considered a mixture of gas and liquid. By tracking the phase fraction, the VOF interface is determined [34]. The relevant parameters at the interface are computed using the following set of equations: ...
As an emerging micro/nanoscale 3D printing technology, Electrohydrodynamic (EHD) printing has undergone rapid development in recent years. However, in most EHD printing processes, voltage is directly applied to both the nozzle and the substrate, resulting in the electric field being influenced by the printing height. This poses challenges for printing three-dimensional curved surface structures. This study presents a comprehensive investigation into the EHD jetting process, utilizing a novel voltage loading method that separates electrodes from both the nozzle and the substrate. Through experimental setups and numerical simulations, this research was conducted to examine the effects of printing height, voltage, and electrode diameter on jetting behavior. The results show that compared to the traditional electrode form, the new voltage loading method will increase the electric field intensity of the liquid surface before ejection by 37.1% and is more conducive to the formation of Taylor cones. It can ensure that the printing fluctuation is less than 2.4% when the printing height varies between 1.5–2.5 times the nozzle diameter, which is more favorable for printing multi-layer structures. The threshold voltage for ejection is provided in this model. When the electrode is reduced, the efficiency of electric field utilization will be further improved, but the acceleration of the jet velocity will cause an increase in droplet size. The findings highlight the method’s capability to maintain consistent droplet sizes and electric field intensities across varying conditions, thereby enhancing printing stability and efficiency. The study’s innovations provide valuable insights for advancing micro/nano 3D printing technologies, emphasizing the potential for improved EHD printing processes in practical engineering applications.
... Sun et al. [22], proposed a combination of the VOF method and the LEVEL-SET method for two-phase flow systems with a large density ratio and viscosity ratio between the two phases to improve the stability and the efficiency of the computation. In addition, in two-phase flows dominated by surface tension, such as the bubble in this paper, there usually exists spurious currents [23,24], for which Bohacek [25] proposed a new surface tension model used in the VOF method to reduce this numerical error. ...
... While a transition from liquid to vapor can happen at temperatures below the saturation temperature, (T sat ), more rapid vaporization will occur if the phase change happens at the boiling point, T sat . In the present study, we only consider phase change due to vaporization as opposed to condensation [15,16]. More important, we will focus on vaporization that is driven by heat transfer, instead of the slower process of evaporation due to vapor concentration gradients [17,18]. ...
A novel simulation framework has been developed in this study for the direct numerical simulation of the aerodynamic breakup of a vaporizing drop. The interfacial multiphase flow with phase change is resolved using a consistent geometric volume-of-fluid method. The bulk fluids are viscous and incompressible with surface tension at the interface. The newly-developed numerical methods have been implemented in the Basilisk solver, in which the adaptive octree/quadtree mesh is used for spatial discretization, allowing flexibility in dynamically refining the mesh in a user-defined region. The simulation framework is extensively validated by a series of benchmark cases, including the 1D Stefan and sucking problems, the growth of a 3D spherical bubble in a superheated liquid, and a 2D film boiling problem. The simulation results agree very well with the exact solution and previous numerical studies. 2D axisymmetric simulations were performed to resolve the vaporization of a moving drop with a low Weber number in a high-temperature free stream. The computed rate of volume loss agrees well with the empirical model of drop evaporation. Finally, the validated solver is used to simulate the aerodynamic breakup of an acetone drop at a high Weber number. A fully 3D simulation is performed and the morphological evolution of the drop is accurately resolved. The rate of vaporization is found to be significantly enhanced due to the drop deformation and breakup. The drop volume decreases nonlinearly in time and at a much higher rate than the empirical correlation for a spherical drop.
... In the VOF model, different fluid components share a set of momentum equations, and the phase interface of each computational unit can be tracked by introducing variable phase volume fractions. To study the corrosion of acid gas and amine liquid with different volume fractions in the pipeline, the VOF model is used for numerical simulation in this study [33][34][35]. The continuity equation, momentum equation and volume fraction equation used in the calculation are shown in Appendix A (Appendix A.1) [36]. ...
In the high sulfur natural gas purification unit, the connecting pipe of a lean/rich amine heat exchanger is extremely susceptible to corrosion due to the acid gas and amine liquid condition. This work numerically investigated the gas–liquid flow and corrosion of the real-scale connecting pipeline with two horizontal sections, one vertical section and four elbow sections. The effect of acid gas holdup on the gas–liquid flow pattern, distribution of velocity and pressure, and corrosion rate was investigated using an experimental validated model. With an increase in the acid gas fraction from 0.03 to 0.12, the flow pattern of the horizontal section changes from bubbly flow to a stratified flow in the horizontal section, while the flow pattern of the vertical section and elbow section keeps bubbling, and the proportion of gas bubbles increases in the vertical section and all elbow sections. The maximum pressure gradient was observed on the top of the horizontal section. The most serious corrosion section was found out on the outlet of the first elbow section where the gas liquid flow starts to stratify, which is consistent with the measured minimum wall thickness. A solution measure for anti-corrosion acid gas in the pipeline was proposed by adding a bifurcated pipe to separate the acid gas in the first horizontal section. The accumulated acid gas was effectively thrown out from the outlet of the bifurcated pipe. This method provides a promising way to eliminate the acid gas in the pipe and avoid forming stratified flow, which is helpful for prolonging the service life of the pipe.
... Datta et al. (2017) used the interface jump approach to numerically study bubble condensation and compared the results with those simulated using empirical correlations. Samkhaniani & Ansari (2016) and Khosravifar et al. (2021) used the Tanasawa phase change model to simulate bubble condensation with and without application of a magnetic field. To improve the accuracy of the surface tension force for bubble condensation simulation, a coupled level set and VOF (CLSVOF) method was developed by Zeng et al. (2015) and Bahreini et al. (2021). ...
Bubble condensation is an important phenomenon in subcooled boiling and its investigation facilitates better understanding of the heat transfer mechanism of subcooled boiling. In this study, thermally controlled bubble condensation near a solid wall is investigated using the volume of fluid (VOF) method. Simulation results show that a condensing bubble can induce a liquid jet towards the wall at high subcooling and low stand-off distance. This liquid jet will develop into a lateral liquid jet and further increase the condensation rate. Although the jet velocity caused by bubble condensation is significantly lower than that caused by cavitation, it outstrips the velocity of natural and Marangoni convections and, therefore, may contribute to the enhancement of subcooled boiling. A dimensionless parameter that considers subcooling, bubble size and stand-off distance is derived to predict the formation and velocity of the liquid jet induced by bubble condensation.
... Owing to their suitability for handling large interfacial areas, a number of studies have used interface capturing/tracking techniques to simulate the condensing of a single bubble rising though a vertical pipe/channel (Jeon et al., 2011;Liu et al., 2015;Owoeye and Schubring, 2015;Pan et al., 2012;Samkhaniani and Ansari, 2016;Sun et al., 2014). Most demonstrate satisfactory agreement with experimental results, where compared, but their use of empirical correlations tuned for such flows renders this largely unsurprising. ...
Nuclear Thermal-hydraulics (NTH) is a key element of Nuclear Power Plant (NPP) design and safety. It is the study of engineering systems where energy from nuclear fuel is transferred by a coolant to a power generation turbine or to the environment, by heat transfer, phase change and flow processes.
Computational modelling of NTH is already a vital part of both the design and safety substantiation of modern NPP. State-of-the-art NTH modelling tools have the potential to enable a level of design and operational optimisation for future NPP beyond anything seen in the past, delivering both improved safety and economic benefits.
NTH shares modelling challenges and tools with many industries where fluid dynamics is important, but perhaps uniquely, has to deal with all of them simultaneously on a huge range of geometrical scales. Moreover, practical NTH computer codes cannot be completely based on first principles, so incomplete knowledge results in uncertainties that must be rigorously quantified and mitigated.
This review highlights a selection of underlying phenomena most important to NPP, including: turbulence; heat transfer; bubble and droplet thermodynamics and transport; flow induced vibration; surface effects and ageing of structures, together with the multiscale aspects linking of all the above. Current practice and procedures by designers, regulators and utilities are outlined, including consideration of uncertainty management and the challenges of scaling from experiments. Classical ‘whole system’ tools are briefly summarised followed by more detailed discussion on finer grained modelling by 3D Computational Fluid Dynamics (CFD). This review also includes sections summarising emergent technology and international benchmarks and projects.
... The VOF class has a non-sharp character, meaning it produces a smeared interface between phases, resulting in the nonaccurate calculation of interfacial properties and generating spurious currents. The existence of non-physical spurious currents leads to the increased interfacial mass transfer while simulating condensation and evaporation [35][36][37][38][39]. The mentioned scenario contributes to high numerical errors in such simulations and can be encountered as the chief shortcoming of VOF. ...
A benchmark study is conducted using isoAdvection as the interface description method. In different studies for the simulation of the thermal phase change of nanofluids, the Volume of Fluid (VOF) method is a contemporary standard to locate the interface position. One of the main drawbacks of VOF is the smearing of the interface, leading to the generation of spurious flows. To solve this problem, the VOF method can be supplemented with a recently introduced geometric method called isoAdvection. We study four benchmark cases that show how isoAdvection affects the simulation results and expose its relative strengths and weaknesses in different scenarios. Comparisons are made with VOF employing the Multidimensional Universal Limiter for Explicit Solution (MULES) limiter and analytical data and experimental correlations. The impact of nanoparticles on the base fluid are considered using empirical equations from the literature. The benchmark cases are 1D and 2D boiling and condensation problems. Their results show that isoAdvection (with isoAlpha reconstruct scheme) delivers a faster solution than MULES while maintaining nearly the same accuracy and convergence rate in the majority of thermal phase change scenarios.
... For numerical simulation of two-phase flows with heat transfer in absence or presence of phase change, various forms of the energy equation are used in the literature. Most common are formulations in terms of a transport equation for temperature, both in (nominally) sharp interface methods such as VOF [54][55][56] , LS [31,32] and CLSVOF [57] , and in the diffuse interface context of phase field methods [58][59][60][61][62][63][64][65] . However, implementations differ in two respects. ...
We extend a diffuse interface phase-field method for two-phase flow simulations so as to include interfacial heat transfer and the thermal Marangoni effect. The set of governing equations hold non-standard terms, which originally stem from the underlying variational consideration of the total free energy of the two-phase system. It consists of the coupled Cahn-Hilliard Navier-Stokes equations with a temperature-dependent mixing energy term and a temperature transport equation implemented in the OpenFOAM framework. The underlying solver phaseFieldFoam is validated for the test cases of thermocapillary convection in a two-fluid-layer and thermocapillary migration of a drop.
In the main part of the paper, hydrodynamics and heat transfer of a droplet impinging on a heated hydrophobic surface with subsequent bouncing are studied in detail. By comprehensive simulations, the effects of impact velocity, droplet diameter (in mm range) and substrate wettability (contact angle) are investigated. The numerical results for spreading ratio, wall contact time and cooling effectiveness are found to compare well with experiments indicating that the developed code is well suited for heat transfer simulation in two-phase flow. For the maximum spreading ratio, a new generalizing correlation is proposed which models the kinetic energy and energy losses at maximum spreading by two coefficients, which are determined from simulation results. A new correlation is also proposed for the contact time, which takes into account surface wettability. For the time evolution of drop mean temperature, a crossover is observed when comparing simulations with constant and temperature-dependent surface tension, indicating that the inclusion of Marangoni effects increases both, the heat transfer between drop and wall during spreading and the heat transfer between drop and surrounding air after rebound.
... In fact, the reason for this may be the limitation of the empirical correlation phase change model in which the correlation has to be selected based on the working conditions. Another more generic phase change model developed based on the kinetic theory of gases was thus applied to simulate bubble condensation in recent years [17][18][19][20] . Lee model is a classic example of this type of phase change model [21] , which is widely used in studies of boiling and condensation. ...
Determining the empirical coefficient and correlation used in phase change model (such as Lee model and empirical correlation model) is one of challenges for the simulation of two-phase flow. To solve this issue in simulation of bubble condensation using volume of fluid (VOF) method, a new phase change model is developed by coupling Lee model and machine learning method, and is termed as ANN-Lee model in this study. The formulation of the empirical coefficient in Lee model is derived based on energy conservation equation. By learning from data collected from previous experiments or generated by empirical correlations, an artificial neural network (ANN) model is trained to calculate the empirical coefficient in each simulation time step. In verified cases of bubble condensation, the ANN-Lee model well predicts the bubble condensation process without concern for the selection of empirical coefficient or correlation in the phase change model. Even using coarse mesh, it can still achieve a comparably accurate prediction as the fine-mesh case. The present simulation results support the feasibility of applying machine learning method for improving the computational fluid dynamics (CFD) prediction of two-phase flow with phase change.
... Each of these tracking methods has strengths and weaknesses, such that no clear gold standard has emerged that is applicable to the wide range of possible multiphase flow phenomena [89][90][91][92]. However, the existence of spurious current in the interface using the VOF technique as well as robustness and efficiency of the level set makes the level set method the best candidate for evaporation-driven solid particles agglomeration processes like drying of suspension droplets [93][94][95]. ...
Suspension plasma spray is a powerful coating technique for depositing high-quality thermal barrier coatings with promising mechanical and physical properties while taking advantage of the well-established atmospheric plasma spray process. In this process, fine ceramic particles are suspended in liquids such as water or ethanol before injection into a plasma jet. The heat from plasma evaporates the carrier liquid of injected suspension droplets and leads to an agglomeration of the particles. The agglomeration process plays a crucial role in the state of particles before impacting a substrate and, consequently, the mechanical properties of the coating. In this work, numerical models for simulating different cases of drying of a single suspension droplet in processes with a high evaporation rate like suspension plasma spray are devised. The models use a Lagrangian method for tracking suspended solid particles and the Eulerian method for the liquid phase. These models not only demonstrate droplet distortion during evaporation but also predict solid particles behavior suspended in the droplet. The numerical models can describe consecutive states of the agglomeration process, including droplet shrinkage, particle accumulation on droplet surface, and buckling. Also, the numerical analysis sheds more light on the complex phenomena of buckling, especially the interaction of the droplet interface and suspended solid particles, and different types of suspension droplet buckling. The numerical results reveal that the role of capillary forces in the shape of agglomerated particles is significant. It is found that particle-induced surface pressure drives the buckling of the suspension droplet. It is also shown that the particle-induced surface pressure reaches a threshold value at the onset of buckling and overcomes surface tension. Finally, the models have been validated by comparing the simulation results with designed experiments. The numerical results are in good agreement with the experimental ones, both qualitatively and quantitatively.
... The condensing bubble was keeping its spherical shape because of small size and high surface tension forces during its rise. Table 6 also shows the comparison of shapes with past numerical works (Zeng et al. [33] and Samkhaniani and Ansari [34]). ...
This chapter introduces an advanced and new type of Three-Dimensional (3D) numerical method called the InterSection Marker (ISM) method. The ISM method - a hybrid Lagrangian–Eulerian 3D front-tracking algorithm specifically crafted for multi-phase flow simulation. The method was used to simulate rising vapour bubble behaviour in Convective boiling conditions. Two applications: bubble growth and bubble condensation due to the convective action, were investigated. Numerically obtained bubble properties, such as size, shape and velocity, are compared well against the past works, and the ISM method proved to be an efficient numerical tool for the interface tracking of multi-phase flow CFD simulations involving heat and mass transfer.
... The bubble lifetime is considered the time it takes for the bubble to condense completely. The researchers like Zeng et al and Samkhaniani et al tried to capture interface by calculating the gradient of volume fraction and smoothed the curvature to control the spurious currents [7,8]. Another prominent reference in this area is the work done by Tian et al, who solved the steam bubble condensation problem using a moving particle semiimplicit (MPS) method [9]. ...
... The bubble lifetime is considered the time it takes for the bubble to condense completely. The researchers like Zeng et al and Samkhaniani et al tried to capture interface by calculating the gradient of volume fraction and smoothed the curvature to control the spurious currents [7,8]. Another prominent reference in this area is the work done by Tian et al, who solved the steam bubble condensation problem using a moving particle semi-implicit (MPS) method [9]. ...
Evaporation and condensation phenomena play a significant role in many of the nuclear, biochemical, and thermal processes
in industrial applications. It is a complicated phenomenon as it undergoes both heat and mass transfer processes along with the
complexities involved in the interfacial regions of vapor and liquid phases. Several experimental works have been carried out in the
recent past to understand the condensation process in detail. However, understanding the phenomenon using computational technique is
more advantageous as the interfacial mass transfer between gas and liquid can be modelled accurately. In the present work, condensation
of a saturated vapor bubble in the sub-cooled liquid is studied, and various factors that influence the bubble shape change and the bubble
lifetime, are evaluated. The analysis is carried out using the ‘Multi-Fluid Volume of Fluid’ (VOF) and ‘Thermal Phase Change’ (TPC)
models implemented in ANSYS Fluent commercial CFD solver. A detailed study is performed to obtain the best approach for calculating
interfacial area density using a ‘user-defined function’ (UDF), and the advantage of the node-based gradient calculation method is
exhibited. The numerical results obtained for the history of bubble shape and bubble lifetime are validated against the experiment and
previously published works with good accuracy. The paper also elaborates on how the initial bubble diameter, the subcooling temperature,
and the system pressure affects the shape and lifetime of the bubble during the condensation process.
... For a detailed local heat trans fer resolution, this coefficient should also differ within the simulation domain, depending on the flow conditions and mesh resolution. Despite these issues, both models can lead to good results with the right model calibration [28][29][30][31] . ...
The use of annular low-finned tubes in tube bundle condensers greatly increases the efficiency. This enables enhanced heat coupling within chemical plants, reducing the overall CO2 emission and power consumption. Due to the complex geometry of these tubes, no generalized condensation model is present so far. In this study, we use highly resolved computational fluid dynamics simulations to investigate pure substance condensation on said tubes with a condensation model which is independent of empirical parameters. Within these simulations, the condensate film is fully resolved and heat transfer coefficients are calculated providing the complete information about the condensation process on annular low-finned tubes for the first time. Additionally, a parameter study for the incline of the annular fin is provided. Therefore, computational fluid dynamics is used to predictively evaluate the influence of a single fin parameter, the incline of the fin, of annular low-finned tubes, for the first time. The simulations provide information about the film thickness along the fin flank and the flooding behavior of the tubes. An accurate fluid dynamic behavior of the two-phase flow is gained. Furthermore, the resulting heat transfer coefficients stand in excellent agreement to experimental data.
... Each of these tracking methods has it is strengths and weaknesses, such that no clear gold-standard has emerged that is applicable to the wide range of possible multiphase flow phenomena [29][30][31][32]. However, existence of spurious current in in the interface using the VOF technique as well as robustness and efficiency of the level set makes the level set method the best candidate for evaporation-driven solid particles agglomeration processes like drying of suspension droplet [33][34][35]. ...
A three-dimensional model based on Fast Interface Particle Interaction (FIPI) is developed for drying a single suspension droplet in processes with a high evaporation rate. The numerical model is able to describe consecutive states of the agglomeration process including droplet shrinkage, particles accumulation on droplet surface, and buckling. Also, the three-dimensional analysis sheds more light on the complex phenomena of buckling specially interaction of droplet interface and suspended solid particles. The model uses a Lagrangian approach for tracking suspended solid particles and Eulerian approach for the liquid phase. It is found that particle-induced surface pressure drives the buckling of suspension droplet. It is shown that the particle-induced surface pressure increases during evaporation until it reaches a threshold value at the onset of buckling. When the surface pressure is larger than surface tension, deformation of droplet originates in locations with lower concentration of particles.
... Some researchers simulated bubble motion and interface interaction with ambient liquid flow by this method [105,112]. Lagrangian-Euler methods are suitable for the case requiring an accurate interface curvature [99,113], but may not be suitable for free boundaries with significant deformation [102], and it would be difficult to sustain the thickness of the interface with the satisfaction of mass conservation [114]. A method called arbitrary Lagrangian-Eulerian (ALE) interface tracking was developed to alleviate the significant distortion of the boundary [115]. ...
It is common to empirically correlate volumetric mass transfer coefficient kLa for predicting gas-liquid mass transfer in industrial applications, and the investigation of single bubble mass transfer is crucial for a detailed understanding of mass transfer mechanism. In this work, experiments, models and simulations based on the experimental results were highlighted to elucidate the mass transfer between single bubbles and ambient liquid. The experimental setups, measurement methods, the mass transfer of single bubbles in the Newtonian and the non-Newtonian liquid, models derived from the concept of eddy diffusion, the extension of Whitman’s, Higbie’s and Danckwerts’ models, or dimensionless numbers, and simulation methods on turbulence, gas-liquid partition methods and mass transfer source term determination are introduced and commented on. Although people have a great knowledge on mass transfer between single bubbles and ambient liquid in single conditions, it is still insufficient when facing complex liquid conditions or some phenomena such as turbulence, contamination or non-Newtonian behavior. Additional studies on single bubbles are required for experiments and models in various liquid conditions in future.
... The gas−liquid interface is determined with a gas volume fraction of 0.5 to get the maximum bubble thickness. 30 Table 4 shows comparisons of the maximum bubble thickness between experimental data and the simulations. The comparison shows that the simulations are in good agreement with the literature results, indicating that the model is suitable for predicting bubble−electrolyte twophase flow in an aluminum reduction cell. ...
In contrast to the original form of anode, the perforated anode is a new kind of anode that can significantly reduce the bubble thickness while maintaining a stable electrolysis process. The bubble movement was simulated within physical and mathematical models of the flow field in the anode-cathode distance (ACD) area, in which the electrolyte solidification zone in the anode perforations was treated creatively as a porous medium. The flow field distribution and the bubble layer thickness in the ACD area were simulated. The influence of the process parameters, such as the electrolyte temperature and ACD, on the flow field was analyzed. The results show that, compared with the regular anode and slotted anode, the use of perforated anode reduces the thickness of the bubble layer by approximately 1.63 mm and1.06 mm, respectively. The velocity of the electrolyte is positively correlated with the electrolyte temperature, anode width and bubble layer thickness. The immersion depth of the anode and the inter-anode gap have little effect on the bubble thickness and flow field.
The phase change model has recently attracted attention for use in flow-boiling numerical simulation research. Comparison and evaluation of the calculation accuracies and resource consumptions of phase change models are essential for developing an efficient and high-precision phase change model. In this study, the Dong and Chen models, were added to the FLUENT software as two new models by introducing a unique user-defined function (UDF). The two unique models and the Lee model served as the foundation for numerical research, and the values of dependabilities and properties for flow and heat transmission predicted by these models were compared. Visual studies and flow-boiling heat transfer correlations were used to validate the results. The results reveal that the Chen model, which considers the active nucleation density site of bubbles, has a significant advantage over the other two models in terms of predicting flow characteristics. The Lee and Dong models are better suited for forecasting the changing tendency of the heat transfer coefficient, whereas the values obtained with the Chen model are closer to the reference values for the Liu–Winterton correlation. Besides, the two novel models also have higher computational costs.
Multiphase Computational Fluid Dynamics (MCFD) based on the two-fluid model is considered a promising tool to model complex two-phase flow systems. MCFD simulation can predict local flow features without resolving interfacial information. As a result, the MCFD solver relies on closure relations to describe the interaction between the two phases. Those empirical or semi-mechanistic closure relations constitute a major source of uncertainty for MCFD predictions.
In this paper, we leverage a physics-informed uncertainty quantification (UQ) approach to inversely quantify the closure relations’ model form uncertainty in a physically consistent manner. This proposed approach considers the model form uncertainty terms as stochastic fields that are additive to the closure relation outputs. Combining dimensionality reduction and Gaussian processes, the posterior distribution of the stochastic fields can be effectively quantified within the Bayesian framework with the support of experimental measurements. As this UQ approach is fully integrated into the MCFD solving process, the physical constraints of the system can be naturally preserved in the UQ results. In a case study of adiabatic bubbly flow, we demonstrate that this UQ approach can quantify the model form uncertainty of the MCFD interfacial force closure relations, thus effectively improving the simulation results with relatively sparse data support.
Improvement of heat and water management in gas diffusion layers (GDL) is a critical issue to high-performance proton exchange membrane fuel cells (PEMFC). In this study, we develop a gas–liquid-solid coupled solver to simultaneously model the liquid water transport, vapor condensation, conjugate heat transfer, electric conduction and their interactions. A stochastic method is employed to reconstruct the 3D structural GDL. The compression effect on the geometry during assembly is included by applying a 10% compression deformation before converting to the solid fibrous zone in the simulation. The micro-porous layer (MPL) cracks are assumed to be the intake paths of the water transport. The impacts of the liquid water distribution on the heat transfer are investigated. For the whole heat transfer process, the heat conduction is the major approach through the solid fibrous layers both in dry and wet GDL, while the water transport accompanied heat conduction and convection are also crucial in wet GDL. However, the effects of water transport on the electrical conduction can be ignored due to the significant differences of the electrical conductivities between water and solid fibrous layers. Besides, the interactions between vapor condensation and heat transfer are explored, it is shown that the temperature of the fibers under the rib is lower than that of other fibers, leading to a higher condensate water saturation and a lager droplet size at the corresponding positions. The results presented here are significantly helpful to deepen our knowledge on the interactions between heat transfer and water transport, and guide the heat and water management in the PEMFC.
Water transport in vapor/liquid form in gas diffusion layers (GDL) of proton exchange membrane fuel cell (PEMFC) are numerically investigated in this study. A stochastic method is employed to reconstruct the 3D structured GDL, then a validated phase change solver is developed and implemented in the OpenFOAM platform to simulate the vapor condensation process. Comprehensive simulations are carried out to analyze the GDL porosity distribution, compressed deformation, mass flow rate, local temperature and contact angle effects on the vapor condensation and transport dynamics. Two GDL with gradient porosities and one with TGP-H-060 type are reconstructed to compare the vapor/liquid-water transport behaviors. It is found that the spatial distribution of the condensate water is comparatively different from the liquid water transport patterns. It reveals that the water transport in liquid form was much more sensitive to the GDL design, while it is more applicable in vapor form. Due to the GDL compression, the vapor/liquid water transport are impeded, especially in the middle layers of the GDL and large velocity separations are detected during the vapor transport. Meanwhile, the results of the parametric analysis indicate that water transport in vapor form provides more options in avoiding water flooding. This study is significant to deepen our understanding on the vapor condensation process and water transport dynamics in GDL, which can further guide the GDL design and optimization.
One of the important aspects in improving the efficiency of electrochemical processes, such as water electrolysis, is the efficient removal of bubbles which evolve from the electrodes. Numerical modelling based on Computational Fluid Dynamics (CFD) can describe the process, provide insights into its complexity, elucidate the underlying mechanisms of how bubbles evolve and their effect as well as aid in developing strategies to reduce the impact of the bubble.
In this paper, a Volume of Fluid (VOF) based simulation framework to study the evolution of hydrogen bubbles in the order of few hundred micrometers, refered to as continuum scale bubbles, is proposed. The framework accounts for the multiphase nature of the process, electrochemical reactions, dissolved gas transport, charge transport, interfacial mass transfer and associated bubble growth. The proposed solver is verified, for two-dimensional cases, by comparison to analytical solution of bubble growth in supersaturated solutions, stationary bubble, rising bubbles and qualitative analysis based on experimental observations of the variations in current based on static simulations. The proposed solver is used to simulate the evolution of a single bubble under various wetting conditions of the electrode as well as the coalescence driven evolution of two bubbles. The results show that as the bubbles detach, its surface oscillates and the shape of the rising bubble is determined by the balance between drag force and surface tension. These surface oscillations, which causes the bubble to get flattened and elongated, results in temporal variation of the electrical current. The reduction of current due to bubble growth is visible only when these surface oscillations have reduced. The simulations also show the current as a function of the position of the bubble in the interelectrode gap. The framework also predicts the increase in current as a result of bubbles leaving the surface which is larger when the process is coalescence driven. The simulations indicate that bubble coalescence is the underlying mechanism for continuum scale bubble detachment.
In this study, the 3D numerical modeling of the condensation of a bubble inside subcooled liquid has been carried out under a uniform magnetic field and the effects of vertical and horizontal magnetic fields on the condensation behavior of the bubbles with initial diameters of 1.008 mm and 4 mm have been studied. The Tanasawa's mass transfer model was used to simulate the condensation process. The terms related to this model and energy equation have been implemented in OpenFOAM solver. The Maxwell equations, scalar magnetic potential equation, and the magnetic boundary conditions were also applied to the solver by coding. The volume of fluid (VOF) method has been used for capturing the interface of the phases. The obtained results show that the magnetic field stretches the bubble along the magnetic field lines. Besides, the magnetic field increases the pressure inside the bubble, which accelerates the condensation of the bubble in comparison with no magnetic field case. For the bubble with a smaller diameter, the vertical magnetic field contributes to faster condensation of the bubble, while for the bubble with a larger diameter, the bubble condenses and disappears faster in the presence of the magnetic field.
In this study, the assessment of five phase change models (Lee model, temperature recovery model, phase field model, heat flux balance model, and empirical correlation model) on the simulation of bubble condensation was investigated using the volume of fluid (VOF) method. The results show that the simulation accuracy of bubble condensation relates to the difference between the interfacial temperature and the saturation temperature. A comparison with the Stefan problem further reveals that the convection heat transfer near the vapor-liquid interface may prevent the convergence of the interfacial temperature to the saturation temperature. The quantitative expressions of interfacial temperature for different phase change models are derived and compared with the simulation results. Furthermore, a recommendation method for rough evaluation of the relaxation coefficient and mesh size in simulations of bubble condensation with the Lee model, phase field model and heat flux balance model is proposed.
In this paper, direct numerical simulation of two-phase incompressible gas-liquid flow is presented. The interface between two-phase is tracked with Volume of Fluid (VOF) method with Continuous Surface Force (CSF) model. Newtonian flows are solved using a finite volume scheme based on the Pressure Implicit with Splitting of Operators (PISO) algorithm. The results of two test cases are presented to assess the correctness of OpenFOAM CFD package codes. First test case includes a single spherical bubble in liquid, extra pressure produced in bubble is compared with Young – Laplace equation, in second case, dynamic of bubble is investigated by comparing the frequency of oscillating elliptic bubble with Lamb equation. Then the terminal Reynolds numbers and shapes of isolated gas bubbles rising in quiescent liquids are compared with data taken from the bubble diagram of Grace.
In this paper the principles of the FOAM C++ class library for continuum mechanics are outlined. The intention is to make it as easy as possible to develop reliable and efficient computational continuum mechanics (CCM) codes: this is achieved by making the top level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object orientation techniques enable the creation of data types which closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modelling in a FOAM computational uid-dynamics (CFD) code is discussed, and calculations performed on a standard test case, that of flow around an square prism, are presented. To demonstrate the exibility of the FOAM library, codes for solving structures and magneto-hydrodynamics are also presented w...
In this study, numerical approach for simulation of mold filling is presented. Polyurethane foam formation includes several complex phenomena such as chemical reactions, heat generation and blowing agent evaporation. Foam properties are variable during formation, foam viscosity increases and conductivity reduces. Foam phase is considered compressible and two phases are immiscible. Foam front will be captured by volume of fluid and appropriate governing equations will be implemented in OpenFOAM. This study prepares a numerical model to reduce several experimental runs with expensive prototypes for mold design.
The performance of the open source multiphase flow solver, interFoam, is evaluated in this work. The solver is based on a modified volume of fluid (VoF) approach, which incorporates an interfacial compression flux term to mitigate the effects of numerical smearing of the interface. It forms a part of the C + + libraries and utilities of OpenFOAM and is gaining popularity in the multiphase flow research community. However, to the best of our knowledge, the evaluation of this solver is confined to the validation tests of specific interest to the users of the code and the extent of its applicability to a wide range of multiphase flow situations remains to be explored. In this work, we have performed a thorough investigation of the solver performance using a variety of verification and validation test cases, which include (i) verification tests for pure advection (kinematics), (ii) dynamics in the high Weber number limit and (iii) dynamics of surface tension-dominated flows. With respect to (i), the kinematics tests show that the performance of interFoam is generally comparable with the recent algebraic VoF algorithms; however, it is noticeably worse than the geometric reconstruction schemes. For (ii), the simulations of inertia-dominated flows with large density ratios yielded excellent agreement with analytical and experimental results. In regime (iii), where surface tension is important, consistency of pressure–surface tension formulation and accuracy of curvature are important, as established by Francois et al (2006 J. Comput. Phys.
213 141–73). Several verification tests were performed along these lines and the main findings are: (a) the algorithm of interFoam ensures a consistent formulation of pressure and surface tension; (b) the curvatures computed by the solver converge to a value slightly (10%) different from the analytical value and a scope for improvement exists in this respect. To reduce the disruptive effects of spurious currents, we followed the analysis of Galusinski and Vigneaux (2008 J. Comput. Phys.
227 6140–64) and arrived at the following criterion for stable capillary simulations for interFoam: where . Finally, some capillary flows relevant to atomization were simulated, resulting in good agreement with the results from the literature.
This article presents a numerical method directed towards the simulation of flows with changes of phase. The volume-of-fluid level set (VOSET) method, which is a new interface capturing method and combines the advantages of both volume-of-fluid (VOF) and level set methods, is used for interface tracking. A difficulty occurs for the problems studied here: the discontinuous velocity field due to the difference between mass-weighted velocity and volume weighted velocity caused by the phase change at the interface. In this article, some special treatment is made to overcome this difficulty. The VOSET method and the developed treatment for the difference between mass-weighted and volume-weighted velocities are adopted to simulate a one-dimensional Stefan problem, two-dimensional horizontal film boiling, and horizontal film boiling of water at near critical pressure. The predicted results in both Nusselt number and flow patterns are agreeable with experimental results available in the literature.
Fromm's second-order scheme for integrating the linear convection equation is made monotonic through the inclusion of nonlinear feedback terms. Care is taken to keep the scheme in conservation form. When applied to a quadratic conservation law, the scheme notably yields a monotonic shock profile, with a width of only 112 mesh.
In the present work experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented. The dynamics of drop impact on liquid surfaces, the shape of the cavity, the formation and propagation of a capillary wave in the crater, and the residual film thickness on the rigid wall are determined and analyzed. The shape of the crater within the film and the uprising liquid sheet formed upon the impact are observed using a high-speed video system. The effects of various influencing parameters such as drop impact velocity, liquid film thickness and physical properties of the liquids, including viscosity and surface tension, on the time evolution of the crater formation are investigated. Complementary to experiments the direct numerical simulations of the phenomena are performed using an advanced free-surface capturing model based on a two-fluid formulation of the classical volume-of-fluid (VOF) model in the framework of the finite volume numerical method. In this model an additional convective term is introduced into the transport equation for phase fraction, contributing decisively to a sharper interface resolution. Furthermore, an analytical model for the penetration depth of the crater is developed accounting for the liquid inertia, viscosity, gravity, and surface tension. The model agrees well with the experiments at the early times of penetration far from the wall if the impact velocity is high. Finally, a scaling analysis of the residual film thickness on the wall is conducted demonstrating a good agreement with the numerical predictions.
A new method for modeling surface tension effects on fluid motion has been developed. Interfaces between fluids of different properties, or "colors", are represented as transition regions of finite thickness, across which the color variable varies continuously. At each point in the transition region, a force density is defined which is proportional to the curvature of the surface of constant color at that point. It is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero. The continuum method eliminates the need for interface reconstruction, simplifies the calculation of surface tension, enables accurate modeling of two- and three-dimensional fluid flows driven by surface forces, and does not impose any modeling restrictions on the number, complexity, or dynamic evolution of fluid interfaces having surface tension. Computational results for two-dimensional flows are given to illustrate the properties of the method.
A stable semi-implicit numerical scheme is developed for solving nonequilibrium, nonhomogeneous two-phase flow problems. The basic two-fluid, six-equation model which contains the interfacial mass, momentum, and heat transfer is solved by a modified IMF technique. During the pressure iteration loop, the changes in pressures as well as the void fractions are computed simultaneously using the mass and the momentum equations of both phases. It is found that by coupling the calculation of the pressure with the void fraction within the same iteration step, the numerical integration of the basic partial differential equations is very stable. Good agreement is obtained between computer code calculations and test data from the two-phase jet impingement experiment. (A)
The most important concepts and definitions referring to a direct contact heat transfer between a continuous liquid and a single evaporating or condensing particle (drobble), are presented. The published studies in this field are reviewed, and the main results are presented in tabular form, separately for theoretical and experimental investigations. The results are discussed separately for evaporation and condensation. A simple physical model for the phase change of a drobble is first put forward. The differential equations of the resulting mathematical model are solved analytically using power functions for heat transfer and resistance laws. Comparison with experimental data from literature shows satisfactory agreement. Finally, further investigations are considered. This work is pertinent to heat exchangers.
Condensation represents the change of phase from the vapor state to the liquid state because of cooling. It is considered one of the most important heat-transfer processes in many energy-conversion systems, such as electric power generation plants. This chapter emphasizes on the areas of condensation heat transfer that have made progress in the past 15 years. It introduces various types of condensation and examines the wettability of the surface. The transport process at the vapor-liquid interface and the arguments on whether the condensation coefficient takes the value of unity are discussed. Furthermore, the chapter reviews dropwise condensation and film condensation in detail. It also describes the techniques of enhancement of condensation heat transfer. The usage of surface tension force is one of the most sophisticated ways for augmentation of condensation because it does not require extra energy. The chapter concludes with discussion of future trends in research on condensation heat transfer.
The single condensing bubble behavior in subcooled flow has been numerical investigated using the open source code OpenFOAM. A coupled Level Set (LS) and Volume of Fluid (VOF) method (CLSVOF) model with a phase change model for condensation was developed and implemented in the code. The simulated results were firstly compared with the experimental results, they were in great agreements, and thus the simulation model was validated. The validated numerical model was then used to analyze the condensing bubble deformation, bubble lifetime, bubble size history, condensate Nusselt number and other interesting parameters with different variables in subcooled flow. The numerical results indicated that the initial bubble size, subcooling of liquid and system pressure play an important role to influence the condensing bubble behaviors significantly and bubble will be pierced when the subcooling and initial diameter reach a certain value at the later condensing stage. The bubble diameter history and condensate Nusselt number were found in good agreement with the empirical correlation. The drag force coefficient was predicted well by introducing a reduced drag coefficient.
This explores downflow condensation in a circular tube both experimentally and computationally using FC-72 as a working fluid. A highly instrumented condensation module is used to map detailed axial variations of both wall heat flux and wall temperature, which are used to determine axial variations of the condensation heat transfer coefficient. The experimental results are compared to predictions of a two-dimensional axisymmetric computational model using FLUENT. The study provides detailed construction of the model, including choice of interfacial phase change sub-model, numerical methods, and convergence criteria. The model is shown to yield good prediction of the heat transfer coefficient. The computed temperature profiles exhibit unusual shape, with steep gradient near the annular liquid film interface as well as near the wall, and a mild gradient in between. This shape is shown to be closely related to the shape of the eddy diffusivity profile. These findings point to the need for future, more sophisticated measurements of liquid film thickness, and both velocity and temperature profiles, to both validate and refine two-phase computational models.
Flow boiling within microchannels has been explored intensively in the last decade due to their capability to remove high heat fluxes from microelectronic devices. However, the contribution of experiments to the understanding of the local features of the flow is still severely limited by the small scales involved. Instead, multiphase CFD simulations with appropriate modeling of interfacial effects overcome the current limitations in experimental techniques. Presently, numerical simulations of single elongated bubbles in flow boiling conditions within circular microchannels were performed. The numerical framework is the commercial CFD code ANSYS Fluent 12 with a Volume Of Fluid interface capturing method, which was improved here by implementing, as external functions, a Height Function method to better estimate the local capillary effects and an evaporation model to compute the local rates of mass and energy exchange at the interface. A detailed insight on bubble dynamics and local patterns enhancing the wall heat transfer is achievable utilizing this improved solver. The numerical results show that, under operating conditions typical for flow boiling experiments in microchannels, the bubble accelerates downstream following an exponential time-law, in good agreement with theoretical models. Thin-film evaporation is proved to be the dominant heat transfer mechanism in the liquid film region between the wall and the elongated bubble, while transient heat convection is found to strongly enhance the heat transfer performance in the bubble wake in the liquid slug between two bubbles. A transient-heat-conduction-based boiling heat transfer model for the liquid film region, which is an extension of a widely quoted mechanistic model, is proposed here. It provides estimations of the local heat transfer coefficient that are in excellent agreement with simulations and it might be included in next-generation predictive methods.
The evaporation and condensation coefficients of water are extensively analyzed considering also data hitherto not taken into account. From the performed evaluation, a decline of both coefficients with increasing temperature and pressure is derived. For water, the condensation coefficients is generally higher than the evaporation coefficient. Evaporation and condensation coefficients exceed 0.1 for dynamically renewing water surfaces, while the analysis reveals coefficients below 0.1 for stagnant surfaces. The influence of impurities and surface active substances, as well as the effect of the dynamic surface tension is discussed.
In the present study, single steam bubble condensation behaviors in subcooled water have been simulated using Moving Particle Semi-implicit (MPS) method. The liquid phase was modeled using moving particles and the two phase interface was set to be a movable boundary which can be tracked by the topological position of the interfacial particles. The interfacial heat transfer was determined according to the heat conduction through the interfacial liquid layer and the coupling between momentum and energy was specially treated. Computational results showed that the bubble experiences various deformations at lower degrees of liquid subcooling while it remains nearly spherical at higher degrees of liquid subcooling. The bubble lifetime is nearly proportional to bubble size and is prolonged at higher system pressures. Bubble lifetime obtained from the MPS method agrees well with the experiments of 10 and 11, however it is lower than the predictions of Sudhoff et al. (1982). The underestimation is caused by severe bubble deformation at lower degrees of subcooling. The present study exhibits some fundamental characteristics of single steam bubble condensation and is expected to be instructive for further applications of the MPS method to evaluate more complicated bubble dynamics problems.
In this study, the behavior of condensing single vapor bubble in subcooled boiling flow within two different vertical rectangular channels has been numerically investigated by using the VOF (Volume Of Fluid) multiphase flow model. The mass and energy transfer model of bubble condensing process induced by the interfacial heat transfer was proposed to describe the interfacial transportation between the two phases. The results of VOF simulations show a good agreements with previous experimental data in the bubble size variation and lifetime. The bubble lifetime is almost proportional to bubble initial size and be prolonged at increasing system pressure. With the increasing of the subcooling, the bubble lifetime reduces significantly, and the effect of mass flux could be negligible. When the bubble size increased, the bubble shape tends to be changed in a large channel. The VOF simulation results of deformation have good agreement with those of Kamei’ experiment and the results of MPS (Moving Particle Semi-implicit) simulation in a larger channel. Furthermore, the initial bubble size, subcooling of liquid and system pressure play an important role to influence the bubble deformation behaviors significantly. The bubble could be deformed sharper with the increasing subcooling and initial diameter, or could breakup when the subcooling and the initial diameter reach a certain value at the last bubble stage. Nevertheless, the trends of bubble deformation will be weakening with the increasing system pressure.
This paper presents the results of visualization experiments that were carried out to investigate the dynamics of vapor bubbles generated in water pool boiling. In the experiments, vapor bubbles were generated on a vertical circular surface of a copper block containing nine cartridge heaters, and the contact angle of the heated surface was used as a main experimental parameter. The experiments were performed under subcooled as well as nearly saturated conditions. To enable clear observation of individual bubbles with a high speed camera, the heat flux was kept low enough to eliminate significant overlapping of bubbles. When the contact angle was small, the bubbles were lifted-off the vertical heated surface within a short period of time after the nucleation. On the other hand, when the contact angle was large, they slid up the vertical surface for a long distance. When bubbles were lifted-off the heated surface in subcooled liquid, bubble life-time was significantly shortened since bubbles collapsed rapidly due to condensation. It was shown that this distinct difference in bubble dynamics could be attributed to the effects of surface tension force.
In the present study, two-dimensional numerical simulation of single bubble dynamics during nucleate flow boiling has been performed using moving particle semi-implicit (MPS) method. A set of moving particles was used to represent the liquid phase. The bubble–liquid interface was set to be a free surface boundary which can be captured according to the motion and location of interfacial particles. The interfacial heat transfer rate was determined by the energy variety of interfacial particles. The bulk liquid velocities investigated ranged from 0.07 to 0.3 m/s. The surface orientations varied from vertical to horizontal through 60°, 45° and 30°. Bulk liquid subcooling varied from 0 to 6.5 °C and wall superheat from 2.0 to 20.0 °C. The computational results show that the bulk liquid velocity and surface orientation influenced the bubble diameter and liftoff time. Bubble would slide along the heater surface before lifting off and the sliding velocity at liftoff increased with an increase in bulk liquid velocity. Bubble dynamic was related to bulk liquid subcooling as well as wall superheat. The numerical results have been compared with the experimental data.
In the present study, we preformed a two-dimensional numerical simulation of the motion and coalescence of bubble pairs rising in the stationary liquid pool, using the moving particle semi-implicit (MPS) method. Moving particles were used to describe the liquid phase and the vapor phase was evaluated using real vapor sate equation. The bubble–liquid interface was set to be a free surface boundary which could be captured according to the motion and location of interfacial particles. The behaviors of coalescence between two identical bubbles predicted by the MPS method were in good agreement with the experimental results reported in the literature. Numerical results indicated that the rising velocity of the trailing bubble was larger than that of the leading bubble. Both of the leading bubble and the trailing bubble rose faster than the isolated bubble. After coalescence, the coalesced bubble showed velocity and volume oscillations. The time of the volume oscillations increased with increasing initial bubble diameter. The wake flow and vortex would form behind the coalesced bubble.
The structure of a steam-water flow in a vertical pipe of 195.3mm inner diameter was studied using novel wire-mesh sensors for high-pressure/high-temperature operation (max 7MPa/286°C). Tests were carried out at pressures of 1 and 2MPa under nearly adiabatic conditions as well as with slightly sub-cooled water (6K at max). Steam was injected into sub-cooled water and condensed during the upwards flow. The evolution of radial gas fraction profiles and bubble size distributions along the pipe in a high-pressure steam-water flow was measured for the first time. The experimental data allow correlating the intensity of steam condensation in contact with sub-cooled water with the structure of the interfacial area and the bubble size distribution, which is very important for the model development. The data were used to test the complex interaction of local bubble distributions, bubble size distributions and local heat and mass transfer. The model considers a large number of bubble classes (50). This allows the investigation of the influence of the bubble size distribution. The results of the simulations show a good agreement with the experimental data. The condensation process is clearly slower, if the injection nozzle diameter is increased (from 1 to 4mm orifices). Also bubble break-up has a strong influence on the condensation process because of the change of the interfacial area. Some modelling errors arise from the uncertainty of the interfacial area for large bubbles and the heat transfer coefficient.
Using holographic interferometry and high-speed cinematography the heat transfer at the phase interface of vapor bubbles condensing in a subcooled liquid of the same substance was measured with ethanol, propanol, refrigerant R113 and water. To evaluate the axisymmetric temperature field around the bubble from the interference fringe field, the Abel integral method is not sufficient. A correction procedure considering the light deflection caused by the local temperature gradient has been developed and applied to calculate the heat transfer coefficient. The measurements were performed in the range 2<Pr<15 and I<Ja<120. Measured data could be well-correlated as functions of the Prandtl and Reynolds numbers for the heat transfer coefficient and as functions of the Reynolds, Prandtl and Jacob numbers for the bubble collapse time.
The capability of the direct volume of fluid method for describing the surface dynamics of a free two-dimensional rising bubble is evaluated using quantities of a recently published benchmark. The model equations are implemented in the open source computational fluid dynamics library OpenFOAM®. Here, a main ingredient of the numerical method is the so-called surface compression that corrects the fluxes near the interface between two phases. The application of this method with respect to two test cases of a benchmark is considered in the main part. The test cases differ in physical properties, thus in different surface tension effects. The quantities centre of mass position, circularity and rise velocity are tracked over time and compared with the ones given in the benchmark. For test case one, where surface tension effects are more pre-eminent, deviations from the benchmark results become more obvious. However, the flow features are still within reasonable range. Nevertheless, for test case two, which has higher density and viscosity ratios and above all a lower influence of the surface tension force, good agreement compared with the benchmark reference results is achieved. This paper demonstrates the good capabilities of the direct volume of fluid method with surface compression with regard to the preservation of sharp interfaces, boundedness, mass conservation and low computational time. Some limitation regarding the occurrence of parasitic currents, bad pressure jump prediction and bad grid convergence have been observed. With these restrictions in mind, the method is suitable for the simulation of similar two-phase flow configurations. Copyright © 2012 John Wiley & Sons, Ltd.
This paper presents a numerical method directed towards the simulation of flows with mass transfer due to changes of phase. We use a volume of fluid (VOF) based interface tracking method in conjunction with a mass transfer model and a model for surface tension. The bulk fluids are viscous, conducting, and incompressible. A one-dimensional test problem is developed with the feature that a thin thermal layer propagates with the moving phase interface. This test problem isolates the ability of a method to accurately calculate the thermal layers responsible for driving the mass transfer in boiling flows. The numerical method is tested on this problem and then is used in simulations of horizontal film boiling.
This paper reports experimental analyses performed for the results of flow visualization in which saturated steam bubbles approximately 10 mm in diameter were injected into quiescent subcooled water. The patterns of bubble collapse were analyzed from photographs selected from a motion picture film and presented as the instantaneous bubble diameter vs. time. An upward motion was imparted to the bubbles by buoyancy, and because of heat transfer and condensation at the liquid-vapor interface, the bubbles diminished in size as they ascended. The time variations of the bubble diameter and position were determined from detailed analysis of the photographs. The experiments were performed for pressure levels from atmospheric to 10â¶Pa and for temperature differences between the saturated steam and subcooled water from 10 to 70°C. From these, the time for bubbler collapse and the average heat transfer coefficient are inferred.
This reference book presents mathematical models of melting and solidification processes that are key to a wide range of heat transfer and industrial applications, and to the effective performance of latent heat thermal energy storage systems (LHTES).
Cover and contents:
http://www.math.utk.edu/~vasili/va/bk/cover-cont-idx.html
In the present study, the PISO algorithm described by Issa (1985), has
been implemented in a finite-volume method which employs Euler's
implicit temporal difference scheme and a hybrid upwind/centered spatial
difference scheme. The developed approach was applied to the circulation
of two cases of axisymmetric laminar flow in circular ducts with abrupt
enlargement. The first case involved an incompressible fluid with an
open duct end, while the second was concerned with a compressible flow
and a closed duct end. It is pointed out that the results of the
computations verify the findings of the analysis conducted by Issa
regarding the accuracy and stability of the algorithm.
An alternative formula is proposed for the flux limiting phase of the
flux-corrected transport (fct) algorithms of Boris and Book. The
advantages of the proposed new formula are three: trivial generalization
to multidimensions without resort to time-step splitting; elimination of
the clipping phenomenon for vanishing velocity; and reduction of the
clipping phenomenon in a finite velocity field. The new method makes
possible for the first time multidimensional FCT calculations for
problems not amenable to time splitting, such as those involving
incompressible or nearly incompressible flow.
Experiments have been carried out to investigate direct contact condensation of saturated vapor bubbles introduced into a quiescent subcooled water environment. The experiments were performed for a range of pressures from atmospheric to 1 MPa, for subcooling from 10 to 70 K, and for initial bubble diameters of about 10 mm. Flow visualization by highspeed motion pictures was based on a frame-by-frame analysis. The photographs show that the successive shapes of the bubbles during their collapse histories proceeded from a sphere to a hemisphere, to an ellipsoid, to a sphere, and finally to collapse. Two-dimensional photographs clearly show that the cavities of the bubbles during their collapse histories proceeded from the bottom to the top. The time to collapse increased with increasing pressure difference. The rising velocities of the bubbles were essentially constant, with an overall range of 20–25 cm/s.
A finite numerical method is presented for the solution of the two-dimensional incompressible, steady Navier-Stokes equations in general curvilinear coordinates. This method is applied to the turbulent flows over airfoils with and without trailing edge separation. The two-equation model is utilized to describe the turbulent flow process. Body-fitted coordinates are generated for the computation. Instead of the staggered grid, an ordinary grid system is employed for the computation and a specific scheme is developed to suppress the pressure oscillations. The results of calculations are compared with the available experimental data.
Motion picture studies of condensation of isopentane bubbles rising in water elucidate the transfer mechanism involved in latent heat transport.
In general, two characteristic regions are noted. In the first region, up to some 80% liquid content, the bubbles deform and oscillate and heat is transferred by turbulent convection. In the second region the rate of transfer is controlled by the resistance of the condensed liquid, and heat is mainly by conduction. The effect of temperature differences between the bubble and the continuous phase (up to 3.5°C.) on the transfer coefficients could not be isolated, whereas that of the initial diameter of the bubble was quite marked.
The results are in agreement with those obtained in earlier studies of evaporating drops in immiscible liquids, indicating the similarity of the basic heat transfer mechanisms.
A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid–liquid combination considered is copper–water. Steady evaporation is modeled and the liquid–vapor interface shape is assumed to be static during evaporation. Liquid–vapor interface shapes in different geometries are obtained by solving the Young–Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid–liquid contact angle, wick porosity, solid–vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.
Volume-of-fluid (VOF) methods are popular for the direct numerical simulation of time-dependent viscous incompressible flow of multiple liquids. As in any numerical method, however, it has its weaknesses, namely, for flows in which the capillary force is the dominant physical mechanism. The lack of convergence with spatial refinement, or convergence to a solution that is slightly different from the exact solution, has been documented in the literature. A well-known limiting case for this is the existence of spurious currents for the simulation of a spherical drop with zero initial velocity. These currents are present in all previous versions of VOF algorithms. In this paper, we develop an accurate representation of the body force due to surface tension, which effectively eliminates spurious currents. We call this algorithm PROST: parabolic reconstruction of surface tension. There are several components to this procedure, including the new body force algorithm, improvements in the projection method for the Navier–Stokes solver, and a higher order interface advection scheme. The curvature to the interface is calculated from an optimal fit for a quadratic approximation to the interface over groups of cells.
An evaporation model compatible with interface-capturing schemes for vapor–liquid flow is presented. The model formulation is largely independent of the specific realization of interface-capturing and relies on a continuum-field representation of the source terms implementable in a broad class of CFD models. In contrast to most other numerical methods for evaporating interfacial flows, the model incorporates an evaporation source-term derived from a physical relationship for the evaporation mass flux. It is shown that especially for microscale evaporation phenomena this implies significant deviations of the interface temperature from the saturation temperature. The mass source-term distribution is derived from the solution of an inhomogeneous Helmholtz equation that contains a free parameter allowing to tune the spatial localization of the source. The evaporation model is implemented into the volume-of-fluid scheme with piecewise linear interface construction. Results are obtained for three analytically or semi-analytically solvable model problems, the first two being one-dimensional Stefan problems, the third a free droplet evaporation problem. In addition, a two-dimensional film boiling problem is considered. Overall, the comparison between the CFD and the (semi)-analytical models shows good agreement. Deviations exist where convective heat transfer due to spurious currents is no longer negligible compared to heat conduction. With regard to the film boiling problem, a similar evaporation pattern as recently identified using a level-set method is found. A major advantage of the developed evaporation model is that it does not refer to intrinsic details of the interface-capturing scheme, but relies on continuum-field quantities that can be computed by virtually any CFD approach.
Motivated by the need for three-dimensional methods for interface calculations that can deal with topology changes, we describe a numerical scheme, built from a volume-of-fluid interface tracking technique that uses a piecewise-linear interface calculation in each cell. Momentum balance is computed using explicit finite volume/finite differences on a regular cubic grid. Surface tension is implemented by the continuous surface stress or continuous surface force method. Examples and verifications of the method are given by comparing simulations to analytical results and experiments, for sedimenting droplet arrays and capillary waves at finite Reynolds number. In the case of a pinching pendant drop, both three-dimensional and axisymmetric simulations are compared to experiments. Agreement is found both before and after the reconnections.
The theory of flux-corrected transport (FCT) developed by Boris and Book [J. Comput. Phys. 11 (1973) 38; 18 (1975) 248; 20 (1976) 397] is placed in a simple, generalized format, and a new algorithm for implementing the critical flux limiting stage' in multidimensions without resort to time splitting is presented. The new flux limiting algorithm allows the use of FCT techniques in multidimensional fluid problems for which time splitting would produce unacceptable numerical results, such as those involving incompressible or nearly incompressible flow fields. The “clipping” problem associated with the original one dimensional flux limiter is also eliminated or alleviated. Test results and applications to a two dimensional fluid plasma problem are presented.
We introduce a new numerical method, called "SURFER," for the simulation of two- and three-dimensional flows with several fluid phases and free interfaces between them. We consider incompressible fluids obeying the Navier-Stokes equation with Newtonian viscosity in the bulk of each phase. Capillary forces are taken into account even when interfaces merge or break up. Fluid interfaces are advanced in time using an exactly volume conserving variant of the volume of fluid algorithm, thus allowing for full symmetry between fluid phases. The Navier-Stokes equation is solved using staggered finite differences on a MAC grid and a split-explicit time differencing scheme, while incompressibility is enforced using an iterative multigrid Poisson solver. Capillary effects are represented as a stress tensor computed from gradients of the volume fraction function. This formulation is completely independent of the topology of interfaces and relatively easy to implement in 3D. It also allows exact momentum conservation in the discretized algorithm. Numerical spurious effects or "parasite currents" are noticed and compared to similar effects in Boltzmann lattice gas methods for immiscible fluids. Simulations of droplets pairs colliding in 2D and in 3D are shown. Interface reconnection is performed easily, despite the large value of capillary forces during reconnection.
Experiments have been carried out to investigate direct contact condensation of saturated steam bubbles introduced into a quiescent subcooled water environment. The experiments were performed for a range of pressures from 10.3 to 62.1 bar (150-900 ), for subcooling from 15 to 100°C, and for initial bubble diameters of about 3mm. The data reduction of high speed motion pictures was based on a frame by frame analysis wherein the coordinates of the bubble perimeter were recorded in digital form and subsequently processed to yield quantitative information about the bubble collapse history and heat-transfer coefficient. The photographs showed that the successive shapes of the bubbles during their collapse histories proceeded from a sphere to a hemisphere to an ellipsoid to a sphere to collapse; short-lived bubbles collapsed as ellipsoids. The time to collapse and the height to collapse increased with increasing pressure and with decreasing temperature difference. The rise velocities of the bubbles were essentially constant, with an overall range of 15-22cm/s. The average heat-transfer coefficients were on the order of 104W/m2·°C (1750 Btu/h·ft2·°F), with only modest variations with pressure level and temperature difference. The instantaneous heat-transfer coefficients did not differ appreciably from the average coefficients.