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Numerical Modelling of Evaporation and Condensation Phenomena
Abstract and Figures
Investigation of interfacial phase change phenomena has been a subject of keen interest
due to the complexities involved in the evaporation and condensation processes. Therefore,
a numerical model based on the Volume of Fluid (VOF) method has been developed
in OpenFOAM software package. This model is capable of simulating evaporation and
condensation phenomena at a liquid-vapor interface subjected to non-isothemal boundary
conditions. This is part of the study to simulate the phase change phenomena in HydroFluoroEther
(HFE-7000) as observed in the Sounding Rocket Compere Experiment 2 (SOURCE 2). SOURCE 2 focuses on the investigation of behaviour of propellants for future cryogenic space missions. The phase change model is first applied to a benchmark evaporation model. The numerical results are in well agreement with theoretical results. Finally, the model was verified on the sounding rocket experiment (SOURCE 2) and a satisfactory comparison of results was obtained.
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... When the value of α is one, this indicates that only liquid is present in the cell. Fig. 1 shows the volume fractions of liquid in each of the cells based on the values of α. [8] ...
... The Reynolds stresses and the turbulent flow field in the RANS are calculated based on the standard k-ε model. The volume POLISH MARITIME RESEARCH, No 4/2023 45 fraction for the two phases, liquid and gas, is calculated using the volume fraction equation in Eq. (2): (2) where the variables xample of the distribution of values in cells [8] umerical approach is employed to calculate the sloshing ssumed that the fluid flow is incompressible, and the turbulent epresented by the Reynolds-averaged Navier-Stokes (RANS) the turbulent flow field in the RANS are calculated based on raction for the two phases, liquid and gas, is calculated using ): ...
... 12]. and n example of the distribution of values in cells [8] numerical approach is employed to calculate the sloshing s assumed that the fluid flow is incompressible, and the turbulent s represented by the Reynolds-averaged Navier-Stokes (RANS) d the turbulent flow field in the RANS are calculated based on e fraction for the two phases, liquid and gas, is calculated using (2): ...
This study investigates the effects of sway and roll excitations on sloshing liquid loads in a tank, using Ansys Fluent software. The model considered in the study is a 1:50 scaled membrane-type tank, based on a KC-1 membrane LNG tank designed by Korea Gas Corporation (KOGAS). The volume of fluid (VOF) method is used to track the free surface inside the tank, and the standard k-ε model is applied to express the turbulent flow of the liquid. To explore the motion of the tank under excitation, a user-defined function (UDF) and a dynamic mesh technique are employed to control the external forces exerted on the tank through its motion. The results, in the form of time series data on the sloshing pressures in the tank under pure sway, roll, and coupled sway-roll, are analysed, with specific ranges for the excitation amplitudes and frequencies. We show that variations in excitation frequency and amplitude significantly influence the sloshing loads. Sloshing loads are found to intensify when the excitation frequency matches the tank’s primary natural frequency, 1.0 ω 1 ′. Furthermore, with coupled sway-roll excitations, the sloshing loads are weakened when the sway and roll are in-phase and are intensified when these are out-of-phase. Fast Fourier transform analysis provides insights into the frequency domain, showing that the dominant frequency is 0.88 Hz and it is approximately equal to the tank’s primary natural frequency, 1.0 ω 1 ′.
... The three-phase flow in an airlift pump is simulated as a two-phase gas-liquid flow of two compressible and immiscible Newtonian fluids. The system is simulated using the volume-of-fluid (VOF) method [7], where the two phases are treated as a single effective fluid. Introducing the VOF indicator function α ( x; t) illustrated in Fig. 1 and defined as [8] ...
... Here, U is the velocity and p total is the total pressure used in VOF solvers in OpenFOAM and defined as [7]: ...
Airlift pumps use compressed gas to transport liquids and solid particles. Due to the lack of theoretical equations for airlift pump design and prediction of its flow regimes, numerical or experimental investigations must be carried out to find the best condition to operate it with high efficiency. For low volumetric fractions of small solid particles, the flow in airlift pumps may be simplified using a two phase approximation in which the solid phase is neglected. Then, the system corresponds to a liquid-gas mixture and its determining equations consist of the Navier-Stokes equation, continuity, energy conservation and the phase transport equation. This paper presents numerical studies on the optimization of air–water flow in an airlift pump. The studies were performed using a built-in OpenFOAM solver for the two-phase flow of two compressible fluids. The results of calculations are presented for different air mass-flow rates. The influence of gas mass flow rates on airlift efficiency was investigated.
... where φ is the volume flux at faces, S f is the face normal vector pointing outwards from the cell, and C α is an adjustable coefficient that determines the magnitude of the compression (usually C α 1) [15]. n f is the interface unit normal vector taken from the phase fraction distribution as: ...
... where δ is a stabilization factor [15]. The artificial interface compression term is an extra term added to the phase fraction evolution equation and is non-zero only when 0 < α < 1, i.e., at the fluid interface, and avoids its numerical diffusion (notice that in reality, the two fluid flow presents a sharp interface) [16]. ...
In the present study, the simulation of the three-dimensional (3D) non-isothermal, non-Newtonian fluid flow of polymer melts is investigated. In particular, the filling stage of thermoplastic injection molding is numerically studied with a solver implemented in the open-source computational library OpenFOAM®. The numerical method is based on a compressible two-phase flow model, developed following a cell-centered unstructured finite volume discretization scheme, combined with a volume-of-fluid (VOF) technique for the interface capturing. Additionally, the Cross-WLF (Williams–Landel–Ferry) model is used to characterize the rheological behavior of the polymer melts, and the modified Tait equation is used as the equation of state. To verify the numerical implementation, the code predictions are first compared with analytical solutions, for a Newtonian fluid flowing through a cylindrical channel. Subsequently, the melt filling process of a non-Newtonian fluid (Cross-WLF) in a rectangular cavity with a cylindrical insert and in a tensile test specimen are studied. The predicted melt flow front interface and fields (pressure, velocity, and temperature) contours are found to be in good agreement with the reference solutions, obtained with the proprietary software Moldex3D®. Additionally, the computational effort, measured by the elapsed wall-time of the simulations, is analyzed for both the open-source and proprietary software, and both are found to be similar for the same level of accuracy, when the parallelization capabilities of OpenFOAM® are employed.
... The time step size in the simulations performed was determined by the Courant Number which determines the propagation speed of information on the mesh (Haider 2013). The ...
Water storage tanks are usually utilized in water distribution systems (WDS) to meet the water demand fluctuations. Long residence periods experienced in these tanks can cause immoderate loss of the disinfectant residual due to the numerous processes that occur in water. Low-level disinfectant residual can encourage microorganism regrowth in the distribution system, leading to unsafe water. Chlorine is the most common disinfectant used to disinfect water supplies. However, variations in the rate of chlorine decay in these storage tanks is one of the greatest limiting factors in ensuring adequate water treatment process and giving guarantee to its efficiency. These variations could be due to some inadequately tested mechanisms of chlorine reactions in bulk fluid, chlorine reactions with storage tank walls, and evaporation. This study presents Computational Fluid Dynamics (CFD) modeling approach to assess the influence of evaporation on residual chlorine in water storage tanks. Simulations together with experimental measurements were performed in laboratories as well as at the water treatment plant in order to gain a better understanding of the influence of evaporation on residual chlorine in water storage tanks. Findings from this study indicate that an increase in the evaporation rate accelerates the rate at which residual chlorine is lost. This study can contribute to the existing literature about monitoring chlorine decay in storage tanks and therefore help the managements of water and sewerage treatment plants to come up with appropriate tools and design of storage tanks. It is concluded that temperature is the main factor influencing evaporation, which in turn causes disappearance of residual chlorine within the water storage tanks.
... The volume of fluid (VOF) method [41] is used in the phase change, and the heat conduction in the wall is not considered. The volume fraction (a l ) for the liquid phase can be obtained from Eq. (1) [42], and the volume fraction (a v ) for the vapor phase from a v ¼ 1 À a l : ...
The oscillatory flow and the heat transfer in two-dimensional pulsating heat pipes (PHPs) with multi-turns were simulated using OpenFOAM. The volume of fluid method was used for the phase change, and the behavior of the working fluid was achieved by considering the mass transfer balance between the evaporation and the condensation. Ethanol was used as the working fluid, and the liquid phase and the vapor phase were assumed to be incompressible. The result revealed that the temperature variation curves did not converge to one pattern according to the number of grids in the symmetric shape of the PHP because the starting time of the working fluid circulation was different. In the PHP with the asymmetric shape, the circulation started earlier than in the PHP with symmetric shape. When the bond number was 0, which means being in zero gravity, the working fluid dried out in the evaporator section of the PHPs with 5 and 10 turns. However, the working fluid still remained in the PHPs with 15 and 20 turns. The numerical analysis performed in this article is expected to help to simulate the flow phenomenon in PHP.
... Among the current multiphase solvers in standard OpenFoam package and also extended solvers, three solvers are selected to evaluate their performance on modeling the thermal driven phase changing inside the cryogenic tanks: interThermalPhaseChangeFoam [21,22] cryoCavitatingFoam [23,31], and compressibleInterFoam [32]. The performance of these solvers in capturing thermally-driven phase change inside the tank and predicting the evaporation rate and tank pressure is summarized below. ...
Liquefied natural gas is predicted to continue its growth as an alternative fuel for the heavy-duty automotive and shipping sector. In recent years, rapid advances in computational fluid dynamics capabilities have led to improvements in the rate of development and cost reduction for cutting edge technology. However, in the field of LNG, currently available tools are not capable of reliably predicting many of the behaviors specific to cryogens and multispecies cryogens. This review surveys the current state of the solvers and studies in the field. Focus is given to variable LNG composition and the corresponding thermophysical properties, tank motion, and thermally-driven phase change as these are the main factors driving LNG behavior in fuel tanks. It is demonstrated that the oversimplification of the LNG composition fails to give full insight into many of the processes taking place. Tank motion is adequately addressed in the current solver state, however, the simultaneous consideration of fluid properties, tank motion, and thermally-driven phase change are the next necessary step. While thermally-driven phase change in cryogenic fluids is well researched, implementation and validation of the physical models in general purpose CFD codes are lacking.
... The discrete Navier-Stokes equations for a transient, 3D, two-phase, isothermal turbulent flow were then solved in the framework of the opensource CFD code OpenFOAM v3.0+ over the calculation grid using the compressibleInterFoam solver, which resorts to a VOF (volume of fluid) phase-fraction based interface capturing approach, and PIMPLE algorithm for pressure-velocity coupling. The resolved equations can be found in (Haider, 2013). Timesteps of 1e -5 to 1e -4 s were chosen (CFL condition C<1) and the k-ε realizable model with wall function was used to account for turbulence. ...
In the present study, the transient air and water flow within a full-scale sprinkler fire protection system filled with pressurized air at idle state (dry pipe) was investigated. Computational Fluid Dynamics (CFD) simulations within the OpenFOAM package were carried out to calculate the air/water flow inside the pipes consequently to the opening of one sprinkler head, accounting for the discharge of air through the sprinkler head, and the inflow of water from a fire pump. A VOF (Volume of Fluids) approach was followed, accounting for the compressibility of air, and turbulence was considered using the k-ε realizable model. Furthermore, pump and sprinkler routines were implemented, taking into account the pump performance curve and the phenomenon of choked flow at the sprinkler head when the exit velocity reaches sonic conditions. Various scenarios were studied, i.e. opening of the sprinkler head before pump activation (also known as single interlock) or opening of the sprinkler head after pump activation (double-interlock). In particular, the time constant of the system, i.e. the time necessary to reach steady-state water flow at the sprinkler head required was assessed for systems of gridded typology under various operating conditions (different initial pressure values in the system).
... Following Haider's derivation [33] of a mixture energy equation for a two-phase VOF model, energy source term due to cavitation i m h H is added to the RHS of the energy equations for the liquid and vapour phases in Eqn (15). This source term comprises interfacial mass transfer rate m , specific enthalpy i h of the liquid/vapour mass that takes part in the phase change process and enthalpy of phase change H .With the addition of these source terms, the mixture energy equation can be rewritten as: ...
... Similar implementations in OpenFOAM (version 2.1.1, The OpenFOAM Foundation, London, UK) have been done by Haider [19] and Kunkelmann [20] in their Ph.D. thesis. Georgoulas et al. [21] implemented an improved VOF method to simulate bubble detachment in pool boiling. ...
In this paper, we apply computational fluid dynamics (CFD) to study the thermodynamic response enhanced by sloshing inside liquefied natural gas (LNG) fuel tanks. An existing numerical solver provided by OpenFOAM is used to simulate sloshing in a model scaled tank of similar form to an LNG fuel tank. The interface area has been estimated for different sloshing regimes on three different numerical grids representing the tank in 3D. Estimating the interface area is done by performing a grid-independence study. In the most severe sloshing conditions, convergence is not achieved. By combining the results from experiments and CFD, it is found that the interface area and the condensation mass flow rate are in phase for the most severe sloshing condition. The existing CFD solver is modified to determine the pressure drop. The simulation results are compared to the experimental data, and the results are acceptable and thereby show a potential in applying CFD to predict the thermodynamic response due to sloshing. By plotting the temperature contours, indications are found that the exchange of cold bulk and saturated liquid due to sloshing has a significant influence on the thermodynamic response.
The paper considers the formation of a ventilated cavity in a flow of water behind a streamlined body. Numerical modeling of the two-phase flow is based on the Volume of Fluid (VOF) method. The system of equations for the water-air mixture consists of the Navier-Stokes equation, continuity equation, energy conservation equation, and diffusion equation, and the equations of state (ideal gas equation, Boussinesq approximation). This system is closed by the Smagorinsky model of turbulence (the model of large eddies). The geometry was designed in accordance with the experimental cavitator using the SALOME open package. The calculation mesh was built by the method of cutting out the geometry from the calculation domain and step-by-step densification near the streamlined body using the snappyHexMesh utility. The results of the simulation of the formation of the air cavity behind the disk cavitator are presented. The influence of the parameters such as air injection velocity, water flow velocity on the formation of the air cavity, its size and stability is illustrated. An approximation dependence is proposed that describes the main parameters of the system. Numerical simulation of the non-stationary problem of the two-phase flow of two compressible fluids without a phase change was done using the compressibleInterFoam numerical model of the open-source package OpenFOAM. The obtained results were analyzed and compared with experimental data. The perspectives of subsequent studies related to the development of a three-phase numerical model using open source packages of programs for accounting for natural cavitation are ilustrated.
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...
The Mass-Conserving Level-Set method combines the efficiency of a Level-Set algorithm with the mass conserving properties of the Volume Of Fluid method. It avoids the work intensive interface construction of the former method and imposes a mass-conserving correction to the distance function of the latter. The interface capturing algorithm implemented in OpenFOAM uses a compressive convection scheme for the evolution of the VOF colour function, as opposed to an interface reconstruction algorithm. Therefore, it can be assumed to match the efficiency of the MCLS
method. Further analysis of the accuracy of the algorithm is required to make a fair comparison. In this report the accuracy will be evaluated for the simulation of incompressible, immiscible two-phase flow in two and three spatial dimensions. Three representative test cases are considered: The advection of a spherical bubble for an imposed, constant velocity field (2D), a rising (buoyant) bubble in a quiescent fluid (2D and 3D) and a stationary bubble in a stationary fluid (2D and 3D). The computed results are compared with results obtained with the Mass-Conserving Level-Set method of [8], benchmark results of [5] and other references. The compressive scheme accurately conserves mass, but shows large spurious currents for the test cases with surface tension. Additionally, the error in the predicted rise velocity of the gas bubble is large in comparison with that of the MCLS method.
Presents introductory skills needed for prediction of heat transfer and fluid flow, using the numerical method based on physical considerations. The author begins by discussing physical phenomena and moves to the concept and practice of the numerical solution. The book concludes with special topics and possible applications of the method.
This book was developed during Professor Ghiaasiaan's ten years of teaching a graduate-level course on convection heat and mass transfer and is further enhanced by his twenty years of teaching experience. The book is ideal for a graduate course dealing with the theory and practice of convection heat and mass transfer. The book treats well-established theory and practice but is also enriched by its coverage of modern areas such as flow in microchannels and computational fluid dynamics-based design and analysis methods. The book is primarily concerned with convection heat transfer. Essentials of mass transfer are also covered. The mass transfer material and problems are presented such that they can be easily skipped. The book is richly enhanced by examples and end-of-chapter exercises. Solutions are available for qualified instructors. The book includes 18 appendices providing compilations of most essential property and mathematical information for analysis of convective heat and mass transfer processes.
This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volume-of-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier–Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.
Several methods have been previously used to approximate free boundaries in finite-difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other methods for treating complicated free boundary configurations. To illustrate the method, a description is given for an incompressible hydrodynamics code, SOLA-VOF, that uses the VOF technique to track free fluid surfaces.
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.