A novel pressure-free two-fluid model for one-dimensional incompressible multiphase flow

Sanderse, Benjamin; Buist, J. F. H.; Henkes, R.A.W.M.

doi:10.1016/j.jcp.2020.109919

Cited by 7 publications

(20 citation statements)

References 11 publications

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“…The PFTFM was introduced by Sanderse et al 27 It is a form of the incompressible two‐fluid model from which the pressure has been eliminated. To this end, (7) is multiplied by

\mathbf{d}

and rewritten as

\mathbf{d}\frac{\partial p}{\partial s}\kern0.5em =-\mathbf{B}\left(\frac{\partial \mathbf{f}}{\partial s}-\mathbf{c}\right)-\mathbf{k}\dot{Q},

with

$$ \mathbf{B}\left(\mathbf{q}\right)=\frac{\mathbf{d}{\mathbf{l}}^T}{{\mathbf{l}}^T\mathbf{d}}=\frac{1}{\hat{\rho}}\left[\begin{...

…”

Section: Formulation Of the Two‐phase Flow Modelsmentioning

confidence: 99%

“…In a recent article by Sanderse et al, 27 it was shown how a four‐equation pressure‐free two‐fluid model (PFTFM) can be derived, by eliminating the pressure using the volume constraint, but otherwise leaving the model in its original conservative form. This model requires no constraints, exhibits the correct shock relations, and allows a time‐dependent volumetric flow rate.…”

Section: Introductionmentioning

confidence: 99%

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Energy‐consistent formulation of the pressure‐free two‐fluid model

Buist

Sanderse

Dubinkina

et al. 2023

Numerical Methods in Fluids

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The pressure‐free two‐fluid model (PFTFM) is a recent reformulation of the one‐dimensional two‐fluid model (TFM) for stratified incompressible flow in ducts (including pipes and channels), in which the pressure is eliminated through intricate use of the volume constraint. The disadvantage of the PFTFM was that the volumetric flow rate had to be specified as an input, even though it is an unknown quantity in case of periodic boundary conditions. In this work, we derive an expression for the volumetric flow rate that is based on the demand for energy (and momentum) conservation. This leads to PFTFM solutions that match those of the TFM, justifying the validity and necessity of the derived choice of volumetric flow rate. Furthermore, we extend an energy‐conserving spatial discretization of the TFM, in the form of a finite volume scheme, to the PFTFM. We propose a discretization of the volumetric flow rate that yields discrete momentum and energy conservation. The discretization is extended with an energy‐conserving discretization of the source terms related to gravity acting in the streamwise direction. Our numerical experiments confirm that the discrete energy is conserved for different problem settings, including sloshing in an inclined closed tank, and a traveling wave in a periodic domain. The PFTFM solutions and the volumetric flow rates match the TFM solutions, with reduced computation time, and with exact momentum and energy conservation.

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“…The PFTFM was introduced by Sanderse et al 27 It is a form of the incompressible two‐fluid model from which the pressure has been eliminated. To this end, (7) is multiplied by

\mathbf{d}

and rewritten as

\mathbf{d}\frac{\partial p}{\partial s}\kern0.5em =-\mathbf{B}\left(\frac{\partial \mathbf{f}}{\partial s}-\mathbf{c}\right)-\mathbf{k}\dot{Q},

with

$$ \mathbf{B}\left(\mathbf{q}\right)=\frac{\mathbf{d}{\mathbf{l}}^T}{{\mathbf{l}}^T\mathbf{d}}=\frac{1}{\hat{\rho}}\left[\begin{...

…”

Section: Formulation Of the Two‐phase Flow Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy‐consistent formulation of the pressure‐free two‐fluid model

Buist

Sanderse

Dubinkina

et al. 2023

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…Moreover, we are not aware of a mathematical analysis of the two-velocity one-pressure model, namely the existence of solutions in a variational setting, stability and convergence of the numerical schemes. In the present study, both velocities (liquid and gaseous phase) are governed by the Navier-Stokes equations for incompressible fluids with single common pressure, interpreted as the Lagrange multiplier (see [30,31] for the incompressibility equation of the mixture). In addition, the mass conservation for the fluids is coupled with the chemical species transport.…”

Section: The Modelingmentioning

confidence: 99%

Numerical Analysis of an Electroless Plating Problem in Gas–Liquid Two-Phase Flow

Pironneau

Shih

et al. 2021

Fluids

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Electroless plating in micro-channels is a rising technology in industry. In many electroless plating systems, hydrogen gas is generated during the process. A numerical simulation method is proposed and analyzed. At a micrometer scale, the motion of the gaseous phase must be addressed so that the plating works smoothly. Since the bubbles are generated randomly and everywhere, a volume-averaged, two-phase, two-velocity, one pressure-flow model is applied. This fluid system is coupled with a set of convection–diffusion equations for the chemicals subject to flux boundary conditions for electron balance. The moving boundary due to plating is considered. The Galerkin-characteristic finite element method is used for temporal and spatial discretizations; the well-posedness of the numerical scheme is proved. Numerical studies in two dimensions are performed to validate the model against earlier one-dimensional models and a dedicated experiment that has been set up to visualize the distribution of bubbles.

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“…Predictions for pressure gradient and mean liquid holdup with the best set of closures presented an average error of 9% and 22%. Sanderse et al [19] have proposed a new pressure-free two-fluid model for the simulation of one-dimensional incompressible multiphase flow in pipelines and channels.…”

Section: Previous Workmentioning

confidence: 99%

A Two-Fluid Model for High-Viscosity Upward Annular Flow in Vertical Pipes

et al. 2021

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Proper selection and application of interfacial friction factor correlations has a significant impact on prediction of key flow characteristics in gas–liquid two-phase flows. In this study, experimental investigation of gas–liquid flow in a vertical pipeline with internal diameter of 0.060 m is presented. Air and oil (with viscosities ranging from 100–200 mPa s) were used as gas and liquid phases, respectively. Superficial velocities of air ranging from 22.37 to 59.06 m/s and oil ranging from 0.05 to 0.16 m/s were used as a test matrix during the experimental campaign. The influence of estimates obtained from nine interfacial friction factor models on the accuracy of predicting pressure gradient, film thickness and gas void fraction was investigated by utilising a two-fluid model. Results obtained indicate that at liquid viscosity of 100 mPa s, the interfacial friction factor correlation proposed by Belt et al. (2009) performed best for pressure gradient prediction while the Moeck (1970) correlation provided the best prediction of pressure gradient at the liquid viscosity of 200 mPa s. In general, these results indicate that the two-fluid model can accurately predict the flow characteristics for liquid viscosities used in this study when appropriate interfacial friction factor correlations are implemented.

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A novel pressure-free two-fluid model for one-dimensional incompressible multiphase flow

Cited by 7 publications

References 11 publications

Energy‐consistent formulation of the pressure‐free two‐fluid model

Energy‐consistent formulation of the pressure‐free two‐fluid model

Numerical Analysis of an Electroless Plating Problem in Gas–Liquid Two-Phase Flow

A Two-Fluid Model for High-Viscosity Upward Annular Flow in Vertical Pipes

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