Two-dimensional Two-phase Flow Research Articles

A three-dimensional curve interface reconstruction algorithm for two-phase fluid flow

The curve interface reconstruction algorithm has received significant attention in the context of two-dimensional two-phase flow. However, it remains absent in the three-dimensional scenario. This paper proposes a novel three-dimensional curve interface reconstruction (CIR) algorithm to address this challenge within structured meshes for the first time. Specifically, a portion of the spherical surface is employed to reconstruct the three-dimensional curve interface segment, with the radius and center coordinates determined by curvature and mass conservation constraints, respectively. To enhance curvature accuracy, a sphere-based iterative reconstruction (SIR) algorithm is proposed to calculate the reconstructed distance function (RDF) for the three-dimensional curve interface. Various tests involving the interface reconstruction of spherical, ellipsoidal, and cubic objects demonstrate that the coupled SIR and CIR (SIR-CIR, simplified by SCIR) method achieves higher accuracy than many popular methods, particularly with coarse mesh resolutions. Additionally, the SCIR method offers the advantages of straightforward implementation and coding for interface reconstruction in two-phase flow research. This advantage results in reduced computational costs compared to the coupled volume-of-fluid and level set (VOSET) method, which also utilizes an iterative method to solve RDF.

A circle-based interface reconstruction algorithm based on the coupled volume-of-fluid and level set method

The interface tends to behave as a circular shape under the effect of surface tension in the two-dimensional two-phase fluid flow. In this study, based on the coupled volume-of-fluid and level set (VOSET) method, an accurate circle-based interface reconstruction (CIR) algorithm for structured meshes is proposed, which features a straightforward implementation procedure. A portion of the standard circle is employed to approximate the curve interface, without the need for complex classification, coordinate transformation, and equation transformation. The radius of this circle is computed simply by the curvature and signed distance at the mixed cell center, and the center of this circle is determined using a straightforward dichotomy method under the mass conservation constraints. Results indicate that the coupled VOSET and CIR (VOSET-CIR) method maintains superior computational accuracy in the signed distance, interface curvature, and dynamic interface reconstruction compared to the coupled VOSET and piecewise linear interface calculation (VOSET-PLIC) method, with accuracy improvements ranging from 34% to 1490% across different test cases. Furthermore, the VOSET-CIR method outperforms the efficient least squares volume-of-fluid interface reconstruction (ELVIRA) and PLIC algorithms in reconstructing random circles and surpasses the quadratic spline based interface reconstruction (QUASI) algorithm in reconstructing random squares. In terms of computational efficiency, except for the initial PLIC algorithm, the time costs of the VOSET-CIR method are substantially lower than those of the ELVIRA and QUASI algorithms, as well as the VOSET-PLIC method.

Influence of embedded structure on two-phase reactive flow characteristics for a small combustion chamber with a moving boundary

In special launch scenarios such as armament and aerospace, the scale of the launch system is severely restricted, which causes unstable combustion of propellant. An embedded structure for the small propulsion system driven by solid propellant is proposed to overcome this problem. This study aims to demonstrate the two-phase flow behaviors and launch safety of the combustion chamber with an embedded structure. A two-dimensional two-phase flow model based on the modified two-fluid theory is developed to describe the detailed two-phase flow behaviors in the combustion chamber during launching. Different from most of the existing studies, the constitutive equations determined from actual physical conditions are used to close the system of continuity equations. The numerical results are compared with that of the experiment to verify the accuracy of the numerical model. On this basis, the launch performance of the embedded structure is investigated. The numerical results indicate that the embedded structure facilitates the ignition process and reduces the risk of excessive pressure, but decreases the muzzle velocity at the same time. In addition, the effect of design parameters on launch safety is further investigated. Design parameters directly affect the launch safety, and the selection of reasonable parameters is a useful method for enhancing the launch performance.

Simulation and Experiment on Elimination for the Bottom-Sitting Adsorption Effect of a Submersible Based on a Submerged Jet

When a submersible is sitting on a seabed, it could lose buoyancy because of the bottom-sitting adsorption effect. In this article, a numerical calculation model and experimental scheme for eliminating the bottom-sitting adsorption effect of under-sea equipment were established. An analysis of the hydrostatic pressure variation on a submersible’s bottom was carried out, and a submerged water jet which was based on the method of soil liquefaction was proposed to solve the problem of reducing hydrostatic pressure. It was shown that a water jet could liquefy soil to restore hydrostatic pressure on the submersible’s bottom, and there was an optimal jet velocity to form the largest liquefied soil thickness. A rectangular pulsed jet was the best way to liquefy soil in terms of efficiency and the liquefaction degree, which can be seen from the calculation of the two-dimensional two-phase flow. Through the calculation of the three-dimensional two-phase flow, it was found that the soil liquefaction developed from the periphery to the center, and a variation in jet liquefaction with the top wall constraint was obtained. Finally, an experiment was carried out to prove that a submerged water jet could eliminate the bottom-sitting adsorption effect of a submersible. The results showed that the submerged jet was an efficient way to liquefy soil, and a submersible could quickly recover hydrostatic pressure on the bottom and refloat up independently.

Performance Analysis of Internal Ballistic Multiphase Flow of Composite Charge Structure

Different charge structures have different interior ballistic performance. Existing research is based on experimental measurements or the lumped parameter method to obtain limited ballistic characteristics, which indirectly impacts the analysis of the parameters’ distribution, requiring a complex modeling solution process. Besides this, the ignition performance of different charge structures needs to be further explored. The disadvantages of previous studies have limited the feasibility of further optimization of the composite charge structure. In this paper, we apply a two-dimensional two-phase flow method based on the Eulerian–Lagrangian model to study the performance of different composite charge structures. First, we establish the mathematical model of different particle types based on interior ballistics, which is directly related to the research foundation of subsequent ballistic performance. Next, we investigate the multi-scale reaction flow of complex charge structures by the two-phase flow method and obtain the distribution of parameters in the chamber. Finally, we conduct a study with different particle charge parameters to explore the sensitivity of ballistic characteristics to structural parameters. The results show that the tubular propellant has good ignition performance in different charge structures, and the ignition consistency can be improved by charging tubular propellant in the center of the chamber. However, more tubular propellants are ineffective at significantly improving ignition performance, and result in a decrease in combustion chamber pressure. These results may be promising for the optimization of various charge structures.

Studying the Marangoni effect in double emulsions with a hybrid multi-relaxation time lattice Boltzmann method–finite difference method

Two-phase mass transfer is a critical process in preparing the inertial confinement fusion target microsphere. It is essential to reveal the effect of Marangoni convection on the flow and mass transfer in double emulsions to prepare high-quality microspheres. This paper develops a two-dimensional two-phase flow and mass transfer model based on multi-relaxation time lattice Boltzmann method and finite difference method. The study of the Marangoni effect within the double emulsion under a shear flow is carried out. The results indicate that the slope parameter (which measures the sensitivity of surface tension to the variation of solvent) and initial solvent concentration crucially affect the mass transfer behavior and the magnitude of the Marangoni convection of double emulsions. When the slope parameter is zero, there is no Marangoni convection in the flow field, the magnitude of the vorticity field is minimal, and solvent diffuses uniformly and slowly to the outer water phase. However, at low values of slope parameter, the Marangoni vortex formed within the emulsion is weak, and few plumes appear in the concentration field; at higher values, the magnitude of the vorticity field increases, and a large number of plumes appear and merge. Compared with the slope parameter, the mass transfer process is less sensitive to the initial solvent concentration. Plumes appear and merge at three different initial solvent concentrations. The time required for double emulsions to develop into equilibrium is inversely proportional to the initial solvent concentration.

Numerical Simulation of Two-Phase Water-Oil Flow in a Horizontal Pipe Using the Smoothed Particle Hydrodynamics Method

In this work, the numerical code DualPhysics, based on the Lagrangian particle and mesh free method Smoothed Particle Hydrodynamics, has been employed to solve the slightly compressible isothermal two-phase water-oil flow. The continuity and momentum equations are solved, and we used the modified Tait equation of state to determine the pressure. To validate the numerical code, we solved the modified Couette flow of two fluids. As a practical case, we solved the isothermal and two-dimensional two-phase water-oil flow. The mixing of the fluids occurs after passing through a 45 degree Y junction placed at the entrance of the horizontal pipeline. Results showed the potential for using the numerical code, although some modifications and alterations are still necessary to solve practical problems.

Study of Liquid Viscosity Effects on Hydrodynamic Forces on an Oscillating Circular Cylinder Underwater Using OpenFOAM®

By neglecting the viscosity of fluid and rotation in flow, the theory of potential flow cannot accurately predict the hydrodynamic forces on the structures under significant viscous effects. In this study, the effects of liquid viscosity on the hydrodynamic forces on a horizontal circular cylinder underwater with a large-amplitude forced oscillation were investigated. The study used a two-dimensional two-phase flow wave tank model based on the viscous fluid theory using the OpenFOAM® package. The numerical calculations were carried out under different types of liquid (i.e., liquid with different viscosities). The liquid viscosity effects are visually shown by comparison of the various frequency components of the hydrodynamic forces on the cylinder, and the magnitude and phase relations of the viscous shear forces and the pressure forces. By analyzing the distribution characteristics of the flow fields around the circular cylinder, the viscous-effect mechanisms are revealed. It is found that the discrepancies of the contributions of viscous shear forces, and the discrepancies of the vortex effects on the phase and magnitude of the pressure forces lead to the obvious differences among the results under different liquid viscosities.

Numerical Simulation of Imported Sediment in a Stilling Basin

Sediment buildup at the bottom of a stilling basin can result in premature drainage of spillway structures and can even lead to dam failure in severe cases. Such failures pose ecological and human safety hazards to downstream areas. To evaluate the sudden discharge and potential dam failure associated with sediment buildup, we developed a two-dimensional two-phase flow simulation model built on a particle-based force balance equation. We compared the flow patterns and energy dissipation effects in the stilling basin at different inlet flows (2, 3, 4.5, and 6.75 m2/s), and the subsequent bottom deposition was compared across different sand discharge mass flow rates (0.1, 0.2, and 0.3 kg/s). The results show that the turbulent energy increased with the increasing inlet unit width flow rate. When more vortices were generated and the flow velocity was reduced significantly, the energy dissipation was more effective. The sediment deposition at the bottom of the stilling basin gradually increased with the decrease of inlet unit width flow and the decrease of the sediment mass flow rate. Meanwhile, at a fixed inlet shape, the change in inlet unit width flow had little effect on the maximum sedimentation height at the bottom of the basin. In addition, the average deposition rate at the bottom of the stilling basin was positively correlated with the inlet sedimentation concentration, and the correlation coefficient could be as high as 0.97. In this two-phase flow method, the error of the simulated value over the theoretical value was less than 10%. This simulation of sediment deposition at the bottom of the stilling basin provides a practical reference for dam managers.

Two-phase flow characteristics of different charging structure in ignition and flame-spreading

To study the influence of flame-spreading behaviour in the ignition process of different charging structures in high-density charge chambers, a visualisation device was designed, and the ignition process of the two charging structures was researched. The flame-spreading process was observed by a high-speed digital camera system and the pressure data was recorded by a data acquisition instrument. According to the experiment, a two-dimensional axisymmetric internal ballistic two-phase flow model was established to simulate the flow process of gas in particle bed based on the Weighted Essentially Non-Oscillatory (WENO) Scheme. The results show that the flow field and flame-spreading status in different charging structures are different. In the full charging structure, the development of the flow field is regular, the flow field in the entire chamber has less fluctuation areas, and velocity vortices only generate during the development of the flow field and when it reaches the wall. However, in the partially charging structure with free space, there are many pressure fluctuation areas in the flow field in the chamber, and the flow field development is also uneven. Pulsating propagation occurs at the interface between particles and free space, which has a great influence on the whole combustion and ignition process. The research results reveal the characteristics of two-phase flow in different charging structures and provide a reference for the actual charging process.

Numerical modeling of local effects on the petroleum reservoir using fixed streamtubes for typical waterflooding schemes

The difficulty of numerical modeling of areal methods of flows redistribution in the oil reservoir is the need for detailed resolution of local hydrodynamic effects and the fine geological structure of the reservoir, which are centimeter-wide, at inter-well distances of the order of several hundred meters. The dimension of computational grids of traditional 3D models of such resolution, even for impact areas containing a small number of injection and production wells, turns out to be excessively large for design calculations. To overcome these limitations, it is proposed to perform a detailed simulation of the flow in two-dimensional cross sections of the reservoir along fixed streamtubes of variable width between each pair of interacting injector and producer wells. Reducing the dimension of the problem allows the use of high-resolution grids to simulate short-term local effects. In this paper, we present an algorithm for constructing a single fixed streamtube between injector and producer, which provides a minimum error in calculating of flow rate and water cut using a two-phase flow problem of reduced dimension along the streamtube. The algorithm is demonstrated by the example of the two-dimensional two-phase flow problem neglecting capillary and gravitational forces in a homogeneous reservoir of constant thickness for three waterflooding elements corresponding to seven vertical well flooding patterns – standard and inverted four-spot, five-spot and seven-spot, as well as staggered line drive. For these waterflooding elements, efficient streamtubes have been constructed, the relative width of which is approximated by piecewise linear functions. On the example of a staggered line drive or five-spot well patterns, the width of the effective streamtube was parameterized for an arbitrary ratio of the sides of the waterflood element. Presented streamtubes can be used as ready templates for subsequent modeling of geological and technical treatments in the relevant elements of the water flooding of the oil reservoir.

Numerical analysis on the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves

The collision of solitary waves is closely related to many physical problems. In this paper, the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves are analyzed using a self-developed two-dimensional two-phase flow model. Advanced Adaptive Mesh Refinement (AMR) grid is adopted to reduce the computational cost. The free surface is captured with the Volume of Fraction (VOF) method combined with Piecewise Linear Interface Calculation (PLIC). The Immersed Boundary (IB) method is used to account for the existence of the barrier. Several benchmark problems including solitary wave propagation, head-on collision of two solitary waves, and solitary wave past a submerged barrier are considered to validate the accuracy of the model. Then the model is utilized to simulate the head-on collision of two solitary waves with the existence of a submerged bottom-mounted barrier. Both the symmetric (two waves with equal amplitudes) and asymmetric (two waves with unequal amplitudes) head-on collisions are investigated. The results with and without the barrier are compared and analyzed in detail. Special attention is paid to the variations of the wave amplitudes and the vortex sheddings.

A prediction method for the performance of a low-recoil gun with front nozzle

Abstract One of the greatest challenges in the design of a gun is to balance muzzle velocity and recoil, especially for guns on aircrafts and deployable vehicles. To resolve the conflict between gun power and recoil force, a concept of rarefaction wave gun (RAVEN) was proposed to significantly reduce the weapon recoil and the heat in barrel, while minimally reducing the muzzle velocity. The main principle of RAVEN is that the rarefaction wave will not reach the projectile base until the muzzle by delaying the venting time of an expansion nozzle at the breech. Developed on the RAVEN principle, the purpose of this paper is to provide an engineering method for predicting the performance of a low-recoil gun with front nozzle. First, a two-dimensional two-phase flow model of interior ballistic during the RAVEN firing cycle was established. Numerical simulation results were compared with the published data to validate the reliability and accuracy. Next, the effects of the vent opening times and locations were investigated to determine the influence rules on the performance of the RAVEN with front nozzle. Then according to the results above, simple nonlinear fitting formulas were provided to explain how the muzzle velocity and the recoil force change with the vent opening time and location. Finally, a better vent venting opening time corresponding to the vent location was proposed. The findings should make an important contribution to the field of engineering applications of the RAVEN.

Numerical investigation of a mixture two-phase flow model in two-dimensional space

A two-dimensional two-phase flow model for gas-liquid mixture is presented. The model takes into account the relative velocity between the gas and liquid phases and is based on conservation equations for gas-liquid mixtures. The mixture model involves balance equations for the relative velocity and is able to handle it without any physical or artificial stabilization in the source terms. The novel aspect of the mixture model is that it is written in a conservative form and ensures the hyperbolicity of the two-phase flow equations. With this regard, the governing equations are solved with finite volume methods. We extend and apply the framework of Godunov methods of centred-type, namely, the FirstOrder Centered (FORCE) and the Slope Limiter Centered (SLIC) methods to the two-dimensional governing equations without any loss of generality in the numerical solutions. An efficient assessment of both the mixture model and the numerical methods is carried out by simulating physical problems available in the literature. Simulations agree well with those in the literature and include new insights that could be used to explain the relative velocity observations. The favourable results suggest that the two-dimensional mixture model simulations can be employed for practical engineering problems of the non-equilibrium type.

A New Interface Identification Technique Based on Absolute Density Gradient for Violent Flows

An identification technique for sharp interface and penetrated isolated particles is developed for simulating two-dimensional, incompressible and immiscible two-phase flows using meshless particle methods in this paper. This technique is based on the numerically computed density gradient of fluid particles and is suitable for capturing large interface deformation and even topological changes such as merging and breaking up of phases. A number of assumed particle configurations will be examined using the technique, including these with different level of randomness of particle distribution. The tests will show that the new technique can correctly identify almost all the interface and isolated particles, and also show that it is better than other existing popular methods tested.

Численный расчет двумерных течений двухфазной жидкости с учетом смачиваемости с помощью квазигидродинамических уравнений

Численный расчет двумерных течений двухфазной жидкости с учетом смачиваемости с помощью квазигидродинамических уравнений

О численном алгоритме для расчета двумерных двухфазных течений с учетом эффекта смачивания на основе квазигидродинамической регуляризации

О численном алгоритме для расчета двумерных двухфазных течений с учетом эффекта смачивания на основе квазигидродинамической регуляризации

Enhancement of heat and mass transfer performance on humidification tower using injection of different carrier gases into water bed

The present study is presented an approach attempting for enhancement of heat and mass transfer between a continuous gas phase and liquid phase in a non-packed humidification towers by injection of different carrier gases such as air, carbon dioxide and helium through water bed. The computational technique utilized was a three-dimensional Navier-Stokes solver in the laminar flow regime with free-surface simulation in Piecewise Linear Interface Construction method to compute density variation on the two-dimensional two-phase flow field and pressure on a water bed. This work studied the influence of the operating conditions such as the water bed temperature and carrier gas type on the overall gas phase heat and mass transfer coefficient. The present study included also determining the overall pressure drop of the carrier gases through water bed, consumed power and humidification efficiency. It has been found that the mass transfer coefficient increases with increasing carrier gas molecular weight. The heat transfer coefficients are more than 5 times for carbon dioxide than air flow and less for helium than air, about 50% flow at water bed temperature 353K. The mass transfer coefficients are more than 2.5 times for helium than air and less for carbon dioxide than air, about 50% at water bed temperature 353K. The obtained maximum humidification efficiency of the helium was about 87%. The pressure drop was about 51.4kPa for helium and 47.2kPa for carbon dioxide at a water bed temperature 353K. The consumed power was about for helium about 45.45W and for carbon dioxide was 41.25W at a water bed temperature 353K. The comparison between the numerical and other experimental results shows a good matching of outlet humidity ratios for air as a carrier gas except that the numerical values were slightly smaller than experimental ones. This may be attributed to the laminar flow computation without including turbulence effects and the two-dimension computational model consideration.

Numerical modeling and investigation of two-phase reactive flow in a high-low pressure chambers system

A high-low pressure chambers system is proposed to meet the demands of low launch acceleration for informative equipment in many special fields such as Aeronautics, Astronautics and Weaponry. A two-dimensional two-phase flow numerical model is established to describe the complex physical process based on a modified two-fluid theory, which takes into account gas production, interphase drag, intergranular stress, and heat transfer between two phases. In order to reduce the computational cost, the parameters in the high-pressure chamber at the instant the vent-holes open are calculated by the zero-dimensional model as the initial conditions for the two-phase flow simulation in the high-low pressure chambers system. The simulation results reveal good agreement with the experiments and the launch acceleration of a projectile can be improved by this system. The propellant particles can be tracked clearly in both chambers and a strong packing of particles at the base of projectile will cause the pressure to rise faster than at other areas both in the axis and radial directions. The length–diameter ratio of the high-pressure chamber (a typical multi-dimensional parameter) is investigated. Different length–diameter ratios can affect the maximum pressure drop and the loss of total pressure impulse through the vent-hole, then the muzzle velocity and the launch acceleration of projectiles can be influenced directly. This article puts forward a new prediction tool for the understanding and design of transient processes in high-low pressure chambers system.

Parametric studies influencing condensation evolution in compressible steam flow

In this paper, the effect of operational and geometrical parameters on the location of condensation onset and the rate of condensations are considered. These parameters are expansion rate of different geometry, inlet stagnation condition and the waves. To do so, a numerical method is presented to solve the two-dimensional two-phase steam flow over a series of geometries (such as nozzles, expansion corners and steam turbine blade-to-blade passages) by means of equilibrium thermodynamics model.