Direct numerical simulation of incompressible multiphase flow with vaporization using moving particle semi-implicit method

https://doi.org/10.1016/j.jcp.2020.109911Get rights and content

Highlights

  • A fully Lagrangian moving-particle based method for incompressible multiphase flows with vaporization.

  • Particle splitting technique to avoid volume difference among particles.

  • Accurate calculation of two-dimensional horizontal film boiling problem.

Abstract

In this paper, the moving particle semi-implicit (MPS) method is developed towards the simulation of multiphase incompressible flows with mass transfer due to vaporization. Traditional MPS method assumes particle volume to be constant and encounters difficulty in modeling vapor-liquid phase change due to abrupt volume change in vaporization process. In the proposed model, particle volume is assumed variable and volume change due to vaporization is considered. Particle splitting technique is developed to avoid large volume difference among particles. Source term accounting for mass transfer rate in vaporization process is developed in the pressure Poisson equation (PPE). Combined with enhanced MPS schemes developed in our previous studies, the numerical method is tested on single rising bubble, one-dimensional Stefan problem, vapor film growth around a sphere without gravity and then used in simulations of two-dimensional film boiling on both horizontal surface and cylindrical surface.

Introduction

Multiphase flows with vaporization can be found in many industrial processes, such as cooling systems, boilers, heat exchangers, etc. However, the evaluation of vaporizing heat transfer and interfacial dynamics largely relies on experiment measurements and empirical models greatly although empirical correlations are limited to specific conditions and details of heat and mass transfer process cannot be measured or observed. Over the last few decades, there has been great interest in developing computational methods to solve multiphase flows with phase change. Accurate direct numerical simulation of the vaporizing phase change allows one to observe the details of such complex phenomenon. Multiphase flows with vaporization are characterized by the discontinuity across the interface with mass and heat transfer caused by phase change. The computation of multiphase flows with vaporization remains one of the most challenging field of computational fluid dynamics.

There are mainly two different approaches to model such type of flow in previous studies employing grid-based methods. The first one is based on moving grid to follow the interface. Welch [1] presented the simulation of a two-dimensional film boiling using moving triangular grids. However, moving grid is unable to cope with topology change of the interface and the simulation is limited to short time. Similar difficulty was encountered by Son and Dhir [2]. The second class is Eulerian based methods on fixed grid with interface tracking or capturing method. Most famous interface tracking methods include front tracking method [3], level set (LS) method [4], [5] and volume of fluid (VOF) method [6]. A front tracking approach was used by Juric and Tryggvason [7] to the simulation of boiling flows. This method was also used by Esmaeeli and Tryggvason [8] to simulate three-dimensional film boiling. Simulation of boiling flows were also carried out by Son and Dhir [9] using a LS approach and by Welch and Wilson using a VOF approach [10]. Tomar et al. [11] investigated bubble formation, growth and departure in film boiling phenomenon using coupled LS-VOF method.

Besides grid-based methods, several grid-free fully-Lagrangian based methods are drawing more and more attention for simulation of fluid flows. Popular grid-free methods include the smoothed particle hydrodynamics (SPH) method [12], moving particle semi-implicit (MPS) method [13] and finite volume particle (FVP) method [14], [15]. FVP is very similar with MPS but introduced the concept of surface and volume for particles for the purpose of handling free-surface flows. These particle methods have been successfully applied in solving various flow problems, including incompressible flows [16], [17], [18], [19], [20], [21], compressible flows [22], [23] and multiphase flows [24], [25], [26], [27], [28]. In simulation of multiphase flows, interfaces are always traced automatically and clearly by moving particles. As a result, no additional effort is necessary to capture or track the interface.

Phase change models have also been developed for MPS and FVP. In MPS and FVP, particles are assumed constant volume thus they are appropriate in modeling melting and solidification phase change. Guo et al. [29] simulated rheological behavior in melting metal using FVP. A viscosity model that considered viscosity changes due to phase changes was introduced. Mahmudah et al. [30] then simulated molten core material mixed with solid particles based on the coupling of FVP and discrete element method (DEM). Recently, Duan et al. [31] calculated corium spreading and crust formulation using a novel MPS algorithm. In their algorithm, viscosity was calculated implicitly to eliminate the numerical creeping of highly viscous fluid. Xiong et al. [32] conducted three-dimensional macro-scale melting based MPS and enthalpy method. Although solid-liquid phase change has been successfully modeled for MPS and FVP, liquid-vapor phase change was rarely mentioned due to abrupt change of volume associated with vaporization and condensation. The most well-known treatment was proposed by Yoon et al. [33] to calculate bubble growth in nucleate pool boiling. In their work uniform temperature and pressure are assumed for the vapor phase so that the field equations were solved only for the liquid phase. The same model was used to investigate bubble dynamics during flow boiling [34]. In SPH context, A.K. Das and P.K. Das [35] used pseudo particles to storage the mass generated due to phase change. Particle redistribution is necessary to ensure enough particles within the cutoff radius of each particle. In [36], an evaporation model was developed based on the weakly-compressible SPH (WCSPH) method for evaporating multiphase flows. Particle splitting and merge technique was employed to avoid large mass difference between particles.

In this study, a novel vapor-liquid phase change model is developed for MPS to solve multiphase incompressible flow with phase change. Different from the model in [33], both the liquid and vapor phase are solved using MPS particles in this new model. In contrast with the evaporating model developed for WCSPH in [36], the proposed model is developed for MPS, in which a semi-implicit algorithm is adopted to solve the pressure field thus more suitable for incompressible flow calculation. To cope with the volume change during vaporization process, volume change is considered and pressure Poisson equation (PPE) is solved with additional source term representing mass transfer rate. Particle splitting technique is developed to avoid large difference between particle volume. Single rising bubble, one-dimensional Stefan problem, vapor film growth around a sphere without gravity and two-dimensional cylindrical and horizontal film boiling are used to validate the MPS method with the proposed phase change model.

Section snippets

MPS method

In this study, bulk fluid is considered incompressible. The following mass conservation and Navier–Stokes equations for incompressible flows are solved:1ρDρDt+u=0DuDt=1ρp+μρ2u+f, where u is the velocity, t is time, ρ is density, μ is viscosity, p is pressure and f represents other forces, such as gravity force.

Vaporization model

To model vaporization, energy conservation is solved. The conservation of specific enthalpy yieldsρDHDt=(kT), where H is the specific enthalpy, k is the thermal conductivity and T is the temperature. Pressure work is neglected as multiphase incompressible flow is considered in this study. Viscous dissipation is also neglected as it considered to be small compared with the heat flux.

Numerical tests

In this section, numerical tests are conducted to validate the developed MPS method for multiphase flow with phase change. The first test is single rising bubble in liquid to demonstrate the capability of the present MPS method to capture interface deformation in multiphase flows without phase change. Then the phase change model is tested by calculating one-dimensional Stefan problem and vapor film growth around a sphere without gravity. Finally, two-dimensional film boiling which is multiphase

Conclusion

In this paper, a Lagrangian moving-particle method based on MPS with vaporization model is developed to calculate boiling flows. Particle splitting technique is developed to handle the volume change during vaporization. This method takes advantage of its Lagrangian nature to trace the interface evolution using moving particles representing different fluid phase. Capability of the MPS in capturing interface deformation is demonstrated by calculating single ring bubble in fluid. One-dimensional

CRediT authorship contribution statement

Xiaoxing Liu: Conceptualization, Methodology, Code development, Writing. Koji Morita: Supervision, Review. Shuai Zhang: Supervision, Review.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (45)

  • Z.G. Sun et al.

    Mass transfer mechanisms of rotary atomization: a numerical study using the moving particle semi-implicit method

    Int. J. Heat Mass Transf.

    (2017)
  • X. Liu et al.

    An advanced moving particle semi-implicit method for accurate and stable simulation of incompressible flows

    Comput. Methods Appl. Mech. Eng.

    (2018)
  • D. Avesani et al.

    A new class of moving-least-squares WENO–SPH schemes

    J. Comput. Phys.

    (2014)
  • X. Liu et al.

    An ALE pairwise-relaxing meshless method for compressible flows

    J. Comput. Phys.

    (2019)
  • X.Y. Hu et al.

    An incompressible multi-phase SPH method

    J. Comput. Phys.

    (2007)
  • A. Mokos et al.

    Multi-phase SPH modelling of violent hydrodynamics on GPUs

    Comput. Phys. Commun.

    (2015)
  • G. Duan et al.

    Stable multiphase moving particle semi-implicit method for incompressible interfacial flow

    Comput. Methods Appl. Mech. Eng.

    (2017)
  • X. Liu et al.

    Accuracy and stability enhancements in the incompressible finite-volume-particle method for multiphase flow simulations

    Comput. Phys. Commun.

    (2018)
  • G. Duan et al.

    A novel multiphase MPS algorithm for modeling crust formation by highly viscous fluid for simulating corium spreading

    Nucl. Eng. Des.

    (2019)
  • J. Xiong et al.

    Lagrangian simulation of three-dimensional macro-scale melting based on enthalpy method

    Comput. Fluids

    (2019)
  • H.Y. Yoon et al.

    Direct calculation of bubble growth, departure and rise in nucleate pool boiling

    Int. J. Multiph. Flow

    (2001)
  • R.H. Chen et al.

    Numerical investigation on bubble dynamics during flow boiling using moving particle semi-implicit method

    Nucl. Eng. Des.

    (2010)
  • Cited by (13)

    • MPS-based axisymmetric particle method for bubble rising with density and pressure discontinuity

      2022, Engineering Analysis with Boundary Elements
      Citation Excerpt :

      Future studies would focus on the extensions of dealing with topological change (e.g. [33,35]) and phase change (e.g. [11,23,30]).

    • GPU-based SPH-DEM Method to Examine the Three-Phase Hydrodynamic Interactions between Multiphase Flow and Solid Particles

      2022, International Journal of Multiphase Flow
      Citation Excerpt :

      In other words, the two different fluid phases are completely resolved, and the spatial distribution of the Lagrangian particles in each phase refers to the region of each phase. Thus, particle-based methods have been widely used in various gas–liquid multiphase flow applications (Chen et al., 2020; Liu et al., 2021; Ming et al., 2017). Moreover, the feasibility of Lagrangian CFD-DEM coupling is potentially high for both resolved and unresolved manner because two numerical models are both based on a Lagrangian methodology.

    • A consistent multiphase flow model with a generalized particle shifting scheme resolved via incompressible SPH

      2022, Journal of Computational Physics
      Citation Excerpt :

      Numerical simulation of multiphase flows is of interest in a variety of engineering, environmental, and industrial applications [1–4].

    • On the free surface boundary of moving particle semi-implicit method for thermocapillary flow

      2022, Engineering Analysis with Boundary Elements
      Citation Excerpt :

      Benefitting from its Lagrangian description, the free surface and the interfacial surface can be directly traced. Since its development, it has attracted extensive attention and has been applied to a wide range of fluid mechanics, including free surface flow [2,3], multi-phase flow [4,5], fluid-solid interaction [6–8], natural convection [9] and phase change [10–12]. Comprehensive and up-to-date reviews on recent developments and applications can be found in Refs. [13,14].

    View all citing articles on Scopus
    View full text