A Consistent Diffuse-Interface Model for Two-Phase Flow Problems with Rapid Evaporation: Addressing Challenges of Density Discontinuities and Interface Dynamics

Core Concepts

This paper introduces a novel diffuse-interface model for simulating two-phase flows with rapid evaporation, addressing challenges like density discontinuities and dynamic interface topologies through consistent level-set transport velocity formulations, reciprocal density interpolation, and a correction term for pressure artifacts in viscous flows.

Abstract

• Bibliographic Information: Schreter-Fleischhacker, M., Munch, P., Much, N., Kronbichler, M., Wall, W. A., & Meier, C. (2024). A consistent diffuse-interface model for two-phase flow problems with rapid evaporation. arXiv preprint arXiv:2401.07805v2.
• Research Objective: This paper aims to develop an accurate and mathematically consistent diffuse-interface model for simulating two-phase flows involving rapid evaporation, focusing on addressing the challenges posed by large density discontinuities and dynamically changing interface topologies.
• Methodology: The authors integrate an incompressible Navier-Stokes solver with a conservative level-set formulation and a regularized representation of discontinuities within a matrix-free adaptive finite element framework. They propose three different formulations for the level-set transport velocity and introduce a reciprocal density interpolation function and a correction term in the Stokes-type constitutive relation to enhance the model's accuracy and consistency.
• Key Findings: The study demonstrates that the proposed model accurately predicts the evaporated mass, velocity jump, and recoil pressure at the liquid-vapor interface. The choice of level-set transport velocity significantly influences the accuracy of interface dynamics predictions, with velocity extrapolation from the liquid or gas phase showing superior performance for strongly curved interfaces. The reciprocal density interpolation function ensures local mass conservation and accurate prediction of the evaporation-induced pressure jump. The correction term in the constitutive relation effectively mitigates pressure artifacts arising from the regularized treatment of evaporative dilation in viscous flows.
• Main Conclusions: The proposed diffuse-interface model provides a robust and accurate framework for simulating two-phase flows with rapid evaporation. The model's ability to handle large density ratios, curved interfaces, and dynamic interface topologies makes it particularly suitable for applications like simulating melt-vapor interactions in laser-based powder bed fusion of metals.
• Significance: This research contributes significantly to the field of computational fluid dynamics by providing a novel and robust model for simulating complex two-phase flow phenomena with phase change. The model's accuracy and efficiency make it a valuable tool for understanding and predicting the behavior of such flows in various engineering and scientific applications.
• Limitations and Future Research: The current study focuses on isothermal conditions. Future research will extend the model to incorporate anisothermal effects, such as evaporative cooling and convective heat transfer, to provide a more comprehensive framework for simulating real-world two-phase flow scenarios.

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A consistent diffuse-interface model for two-phase flow problems with rapid evaporation

by Magdalena Sc... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2401.07805.pdf

Deeper Inquiries

How can the proposed diffuse-interface model be extended to incorporate the effects of surface tension variations and Marangoni convection in two-phase flows with evaporation?

Incorporating the effects of surface tension variations and Marangoni convection in the proposed diffuse-interface model for two-phase flows with evaporation requires several key modifications:

Temperature-Dependent Surface Tension: The model currently assumes a constant surface tension coefficient (α). To account for surface tension variations, α needs to be defined as a function of temperature (T), typically α(T). This introduces a temperature dependency into the surface tension force term (˜f σ) in the momentum equation.

Marangoni Stress Implementation: Marangoni convection arises from surface tension gradients, which induce tangential stresses at the interface. To incorporate this effect, an additional Marangoni stress term needs to be included in the momentum equation. This term is typically proportional to the surface tension gradient (∇sα), where ∇s denotes the surface gradient.

Energy Equation Coupling: The model currently assumes isothermal conditions. To capture the effects of surface tension variations and Marangoni convection, the system of equations needs to be coupled with an energy equation. This equation governs the temperature field within the domain and accounts for heat transfer mechanisms like conduction, convection, and latent heat of evaporation.

Constitutive Model for Surface Tension: A suitable constitutive model for the temperature-dependent surface tension coefficient α(T) needs to be chosen based on the specific fluids involved. Linear or nonlinear relationships can be employed depending on the accuracy required and the temperature range considered.

Numerical Considerations: Incorporating these effects introduces additional nonlinearities into the system of equations. Robust and accurate numerical methods, such as higher-order spatial discretization schemes and implicit time integration methods, might be necessary to ensure stability and convergence of the solution.

By implementing these modifications, the diffuse-interface model can effectively capture the intricate interplay between evaporation, surface tension variations, and Marangoni convection in two-phase flows. This enhanced model can provide valuable insights into complex phenomena like thermocapillary migration, droplet spreading, and thin-film instability, which are crucial in applications like PBF-LB/M, thin-film coating, and spray cooling.

While the diffuse-interface model offers robustness, could a sharp-interface method potentially provide higher accuracy for specific two-phase flow problems with rapid evaporation, and what would be the trade-offs in terms of computational cost and complexity?

Yes, sharp-interface methods can potentially offer higher accuracy than diffuse-interface methods for specific two-phase flow problems with rapid evaporation, but this comes with trade-offs in terms of computational cost and complexity.
Higher Accuracy of Sharp-Interface Methods:

Precise Interface Representation: Sharp-interface methods explicitly track the interface location, eliminating the need for smoothing or regularization. This allows for a more accurate representation of the jump conditions across the interface, particularly for variables like density and velocity, which experience significant discontinuities during rapid evaporation.
Reduced Numerical Diffusion: By explicitly tracking the interface, sharp-interface methods minimize the artificial smearing of the interface that can occur in diffuse-interface methods, especially for high density ratios and rapid interface movements. This leads to a more accurate prediction of the interface dynamics and the overall flow behavior.
Trade-offs in Computational Cost and Complexity:

Meshing Challenges: Sharp-interface methods often require complex meshing techniques to accurately represent the evolving interface. This can be computationally expensive, especially for 3D problems with complex interface topologies and topological changes like droplet breakup or coalescence.
Implementation Complexity: Implementing sharp-interface methods is generally more complex than diffuse-interface methods. They often involve specialized numerical techniques like interface reconstruction, extension of solution fields across the interface, and handling of jump conditions within the discretization scheme.
Computational Cost: While sharp-interface methods can be more accurate, they can also be computationally more expensive than diffuse-interface methods. This is due to the need for finer meshes near the interface, complex mesh adaptation strategies, and the increased complexity of the numerical algorithms.
Choosing the Right Method:
The choice between a sharp-interface and a diffuse-interface method depends on the specific problem being solved and the desired balance between accuracy, computational cost, and implementation complexity.

Diffuse-Interface Methods: Suitable for problems where robustness, ease of implementation, and handling of complex interface topologies are prioritized over the highest level of accuracy.
Sharp-Interface Methods: Preferred for problems where a highly accurate representation of the interface and its dynamics is crucial, and the computational cost and implementation complexity are acceptable.

How can the insights gained from this model be applied to develop more efficient cooling systems for electronic devices, leveraging the principles of two-phase flows and rapid evaporation?

The insights gained from this diffuse-interface model for two-phase flows with rapid evaporation can be applied to develop more efficient cooling systems for electronic devices by leveraging the high heat transfer capabilities of phase change processes. Here's how:

Optimized Microchannel Design: The model can be used to simulate and optimize the design of microchannels used in two-phase cooling systems. By accurately predicting the evaporative mass flux, pressure drop, and heat transfer coefficients, the model can guide the design of microchannels with optimized geometries, flow rates, and working fluids to maximize heat dissipation from electronic components.

Enhanced Boiling Heat Transfer: The model can provide insights into enhancing boiling heat transfer in microchannels. By understanding the influence of surface properties, fluid properties, and flow conditions on bubble nucleation, growth, and departure, the model can help design surfaces with tailored wettability and roughness to promote efficient bubble dynamics and enhance heat transfer.

Effective Microfluidic Cooling Devices: The model can aid in the development of novel microfluidic cooling devices that utilize rapid evaporation for heat dissipation. This includes designing microfluidic evaporators, pulsating heat pipes, and droplet-based cooling systems. The model can predict the performance of these devices under various operating conditions, leading to optimized designs for efficient heat removal.

Nanofluid-Based Cooling Systems: The model can be extended to investigate the use of nanofluids in two-phase cooling systems. Nanofluids, with their enhanced thermal properties, can potentially improve heat transfer coefficients. The model can simulate the behavior of nanofluids during evaporation, considering factors like nanoparticle deposition and stability, to assess their effectiveness in electronic cooling applications.

Thermal Management of High-Power Devices: As electronic devices become more powerful and compact, efficient thermal management becomes increasingly critical. The insights from this model can be applied to develop advanced cooling solutions for high-power electronics, such as CPUs and GPUs, where rapid evaporation and two-phase flow play a crucial role in dissipating large amounts of heat.

By leveraging the predictive capabilities of this diffuse-interface model, researchers and engineers can gain a deeper understanding of the complex physics governing two-phase flows with rapid evaporation. This knowledge can be translated into the design and optimization of innovative and efficient cooling systems for electronic devices, addressing the ever-increasing thermal challenges in modern electronics.