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A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries.

Dong S, Wang X - PLoS ONE (2016)

Bottom Line: Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary.By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results.We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

View Article: PubMed Central - PubMed

Affiliation: Center for Computational & Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, Indiana, United States of America.

ABSTRACT
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

No MeSH data available.


Related in: MedlinePlus

Air jet in water: Temporal sequence of snapshots of the air-water interface at time: (a) t = 22.9997, (b) t = 23.0372, (c) t = 23.0747, (d) t = 23.1122, (e) t = 23.1497, (f) t = 23.1872, (g) t = 23.2247, (h) t = 23.2622, (i) t = 23,2922, (j) t = 23.3222, (k) t = 23.3522, (l) t = 23.3822, (m) t = 23.4197, (n) t = 23.4572, (o) t = 23.5172.Results are obtained using the open boundary condition Eq (3b).
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pone.0154565.g014: Air jet in water: Temporal sequence of snapshots of the air-water interface at time: (a) t = 22.9997, (b) t = 23.0372, (c) t = 23.0747, (d) t = 23.1122, (e) t = 23.1497, (f) t = 23.1872, (g) t = 23.2247, (h) t = 23.2622, (i) t = 23,2922, (j) t = 23.3222, (k) t = 23.3522, (l) t = 23.3822, (m) t = 23.4197, (n) t = 23.4572, (o) t = 23.5172.Results are obtained using the open boundary condition Eq (3b).

Mentions: This different flow state is further illustrated by the temporal sequence of snapshots of the air-water interface shown in Fig 14, which covers a time window between t ≈ 23 and t ≈ 23.5 in the history plot of Fig 13. These results correspond to the open boundary condition Eq (3b). The plots clearly show the breakaway of the air bubble from the wall (Fig 14(a)–14(c)) and the bubble motion across the domain and the upper open boundary (Fig 14(d)–14(k)). The crucial difference, when compared with Fig 10, lies in the following. When multiple free bubbles are present in the domain, the interaction between the leading-bubble wake and the trailing bubble appears to have caused the trailing bubble to accelerate and nearly cath up with the leading one; see Fig 14(e)–14(j). This has also induced significant deformations in the trailing bubble (Fig 14(j)–14(l)), and caused it to subsequently break up (Fig 14(m)–14(o)). As the free bubbles (and their daughter bubbles) quickly move out of the domain, one can observe that another bubble is forming, but still attached to the wall (Fig 14(o)). Consequently, the flow domain will be depleted of free bubbles for a period of time beyond the time instant corresponding to Fig 14(o), until the air bubble attached to the wall breaks free. This scenario is more similar to the one discussed in [6], but is quite different from that shown by Fig 10. From Fig 14(i)–14(k) we can again observe that our method allows the air bubble and the air-water interface to cross the open boundary in a smooth fashion.


A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries.

Dong S, Wang X - PLoS ONE (2016)

Air jet in water: Temporal sequence of snapshots of the air-water interface at time: (a) t = 22.9997, (b) t = 23.0372, (c) t = 23.0747, (d) t = 23.1122, (e) t = 23.1497, (f) t = 23.1872, (g) t = 23.2247, (h) t = 23.2622, (i) t = 23,2922, (j) t = 23.3222, (k) t = 23.3522, (l) t = 23.3822, (m) t = 23.4197, (n) t = 23.4572, (o) t = 23.5172.Results are obtained using the open boundary condition Eq (3b).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4862665&req=5

pone.0154565.g014: Air jet in water: Temporal sequence of snapshots of the air-water interface at time: (a) t = 22.9997, (b) t = 23.0372, (c) t = 23.0747, (d) t = 23.1122, (e) t = 23.1497, (f) t = 23.1872, (g) t = 23.2247, (h) t = 23.2622, (i) t = 23,2922, (j) t = 23.3222, (k) t = 23.3522, (l) t = 23.3822, (m) t = 23.4197, (n) t = 23.4572, (o) t = 23.5172.Results are obtained using the open boundary condition Eq (3b).
Mentions: This different flow state is further illustrated by the temporal sequence of snapshots of the air-water interface shown in Fig 14, which covers a time window between t ≈ 23 and t ≈ 23.5 in the history plot of Fig 13. These results correspond to the open boundary condition Eq (3b). The plots clearly show the breakaway of the air bubble from the wall (Fig 14(a)–14(c)) and the bubble motion across the domain and the upper open boundary (Fig 14(d)–14(k)). The crucial difference, when compared with Fig 10, lies in the following. When multiple free bubbles are present in the domain, the interaction between the leading-bubble wake and the trailing bubble appears to have caused the trailing bubble to accelerate and nearly cath up with the leading one; see Fig 14(e)–14(j). This has also induced significant deformations in the trailing bubble (Fig 14(j)–14(l)), and caused it to subsequently break up (Fig 14(m)–14(o)). As the free bubbles (and their daughter bubbles) quickly move out of the domain, one can observe that another bubble is forming, but still attached to the wall (Fig 14(o)). Consequently, the flow domain will be depleted of free bubbles for a period of time beyond the time instant corresponding to Fig 14(o), until the air bubble attached to the wall breaks free. This scenario is more similar to the one discussed in [6], but is quite different from that shown by Fig 10. From Fig 14(i)–14(k) we can again observe that our method allows the air bubble and the air-water interface to cross the open boundary in a smooth fashion.

Bottom Line: Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary.By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results.We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

View Article: PubMed Central - PubMed

Affiliation: Center for Computational & Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, Indiana, United States of America.

ABSTRACT
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

No MeSH data available.


Related in: MedlinePlus