Computational Multi-fluid Dynamics Research Articles

Effects of nanoparticle size on surface dynamics and thermal performance in film boiling of Al[formula omitted]O[formula omitted] water-based nanofluids

This study investigates the impact of nanoparticle diameter on film boiling in Al2O3 water-based nanofluids along a vertical cylinder, focusing on nanoparticle sizes of 5 nm, 10 nm, 30 nm, and 50 nm. Using a Continuous-Species-Transfer method within a Computational Multi-Fluid Dynamics framework, the behavior of nanoparticles in both liquid and vapor states is simulated, considering Brownian motion and thermophoretic effects. A 2D axisymmetric analysis reveals how nanoparticle sizes influence temperature gradients, nanoparticle concentration patterns, thermophysical properties, and the Nusselt number to assess heat transfer efficiency. Findings indicate that during film boiling, smaller nanoparticles exhibit higher concentrations on the heated wall over time. Additionally, nanofluids with smaller particles demonstrate higher thermal conductivity and viscosity near the heated wall, along with lower surface tension. Interestingly, nanofluids with 30 nm and 50 nm nanoparticles perform closely, indicating a size threshold beyond which further reductions do not significantly enhance boiling heat transfer. In contrast, nanofluids containing 5 nm and 10 nm nanoparticles exhibit markedly superior thermal removal efficiency, underscoring the critical role of nanoparticle size in optimizing film boiling performance.

Influence of nanoparticle shapes in nanofluid film boiling on vertical cylinders: A numerical study

This research explores how nanoparticle shapes affect the thermal behavior of nanofluid film boiling along a vertical cylinder, utilizing a Continuous-Species-Transfer method embedded in a Computational Multi-Fluid Dynamics framework. By modeling the behavior of nanoparticles in both liquid and vapor phases, with considerations for Brownian motion and thermophoresis, a comprehensive 2D axisymmetric analysis is conducted. The analysis focuses on the effects of various Al2O3 nanoparticle shapes – spheres, bricks, blades, cylinders, and platelets – on boiling heat transfer performance. Results demonstrate that while nanoparticle shape has a minimal impact on deposition dynamics, it significantly affects kinematic viscosity, particularly for platelet-shaped nanoparticles. Blade-shaped nanoparticles stand out for their substantial enhancement of thermal transport, as demonstrated by pronounced temperature gradients and elevated thermal conductivity. Furthermore, these nanoparticles contribute to a notable improvement in the Nusselt Number, suggesting enhanced efficiency in boiling heat transfer. This improvement is particularly significant at higher nanoparticle concentrations, where the effects are more pronounced, though not strictly linear when compared to the effects at lower concentrations. Future work will explore different nanoparticle materials, boiling scenarios, and experimental validation.

Nanoparticle migration in nanofluid film boiling: A numerical analysis using the continuous-species-transfer method

Investigating the boiling behavior of nanofluids remains a topic of considerable research interest. The existing theoretical framework often underscores Brownian motion and thermophoresis among the predominant mechanisms that influence nanoparticles' movement within nanofluids. However, most current numerical models addressing nanofluid boiling either neglect these mechanisms or incorporate them inadequately. A comprehensive review of the literature reveals two primary gaps. The larger set of numerical studies on nanofluids boiling does not account for any governing equation for nanoparticle concentration, neglecting the primary mechanisms of nanoparticle movement. The smaller set includes such an equation but limits its application to the vapor domain, thereby overlooking the liquid nanofluid phase. Moreover, in the context of film boiling involving nanofluids, an insulating vapor film forms between the nanofluid and the heated surface. This vapor film is dynamic, experiencing evaporation at its outer boundary, leading to an increase in nanoparticle concentration at the vapor-liquid interface—another aspect always neglected in existing numerical models. To address these research gaps, this study introduces a specialized governing equation employing the Continuous-Species-Transfer method within the framework of Computational Multi-Fluid Dynamics. Importantly, it also incorporates governing equations for thermophoresis and Brownian motion to account for the motion of nanoparticles. The method's efficacy is further corroborated by solving a two-dimensional axisymmetric film boiling problem on a vertical cylinder, with results aligning well with analytical studies that consider Brownian motion and thermophoretic behavior. Overall, the study fills a critical gap in the literature by providing a comprehensive tool for examining complex interfacial behaviors in nanofluid film boiling.

On ghost fluid method-based sharp interface level set method on a co-located grid and its comparison with balanced force-based diffuse interface method

This paper, on Computational multi-Fluid Dynamics (CmFD) development, presents an extension of the Ghost Fluid Method (GFM)-based Sharp Interface Level Set Method (SI-LSM) (originally proposed on a staggered grid) for a co-located grid system. Further, this paper presents a comparative study for the GFM-based SI-LSM and a balanced force method (BFM)-based Diffuse Interface Level Set Method (DI-LSM). The BFM-based DI-LSM avoids a pressure-interfacial force decoupling, during the implementation of the MIM, by a proper-discretization of the surface tension term; not needed for the single-phase flow. Whereas, the GFM-based SI-LSM implicitly couples two immiscible, incompressible fluids via interface jump condition, which makes the Momentum Interpolation Method (MIM) for the two-fluid flow same as that for a single-fluid flow. A unified, for both SI-LSM and DI-LSM, mathematical and numerical formulations are presented. Order of accuracy is demonstrated in-between first-order and second-order; similar to that reported earlier for the various CmFD methods. Finally, validation and relative-performance study are presented for four test cases: static droplet, dam break, drop coalescence, and Rayleigh-Taylor instability. For the static droplet, the relative-performance of the present SI-LSM as compared to the DI-LSM is found similar to that in the literature for SI-VOF (Volume of Fluid) method as compared to DI-VOF method. For the various test cases, superior performance is demonstrated for the SI-LSM as compared to DI-LSM. This paper presents a broader perspective to the MIM for a single-versus-two fluid-flow and diffuse-versus-sharp approaches; and a novel GFM-based SI-LSM on a co-located grid.

PERFORMANCE OF SHARP-VERSUS-DIFFUSE INTERFACE-BASED LEVEL SET METHOD ON A STAGGERED-VERSUS-CO-LOCATED GRID FOR CMFD

The present work is on comparison of computational performance for various level set methods (LSMs): diffuse interface level set method on staggered grid (DI-LSM<sub>stag</sub>), sharp-interface level set method on staggered grid (SI-LSM<sub>stag</sub>), diffuse interface level set method on co-located grid (DI-LSM<sub>col</sub>), and sharp interface level set method on co-located grid (SI-LSM<sub>col</sub>). Even though the implementations of the diffuse and sharp interface (DI and SI) approaches on staggered grid are straightforward, an additional pressure-interfacial force balance needs to be ensured on the co-located grid. This is established here with balanced force method (BFM) for the DI-LSM and ghost fluid method (GFM) for the SI-LSM. Computational performances of these LSMs are presented for a variety of computational multi-fluid dynamics (CMFD) problems: static drop, dam break, rising bubble, falling droplet, and droplet coalescence. Greater accuracy is found with SI-LSMs for the static drop, dam break, and rising bubble, whereas for the other problems, both SI-LSM and DI-LSM result in almost the same accuracy. Smaller computational time is taken by the SI-LSM for rising bubble and falling droplet, and by DI-LSM for the dam break and droplet coalescence. Comparing between grid systems, co-located grid resulted in greater accuracy for all the problems except falling droplet, for which both grid systems resulted in similar accuracy, whereas, a smaller computational time is taken by the co-located grid for rising bubble and falling droplet, and by the staggered grid for dam break and droplet coalescence. Overall, SI-LSM on the co-located grid shows better results with a slight increase in computational time as compared to the other LSMs, and is a suitable alternative to the staggered grid.

Integrating supervised learning and applied computational multi-fluid dynamics

The transition from iterative methods of engineering design towards physics-based modeling has been assisted by the advent of Computer-Aided-Engineering. However, post-processing of simulation results, based on a standard workflow providing base-case simulations complemented by selected operating conditions, has changed little. In this work, we propose a new paradigm for handling simulation data by deploying machine learning to encompass a wide spectrum of operating conditions, bypassing the need for additional simulations. This hybrid physics-based and data-driven modeling procedure yields to what we refer to as a Simulation-based Digital Twin. In this paper, we make the case for Computational Fluid Dynamics in multiphase flow systems, although the workflow can be generalized to any other computational engineering method. We quantify the computational speed-up to conclude that the combination of these two fields generates potential for improvement on the conventional methods used in the broad area of computational engineering.

Experimental and numerical investigation of local bubble parameters for subcooled flow boiling in a pressurized annulus

The wall boiling models adopted in the Computational Multi-Fluid Dynamics (CMFD) tools rely on empirical correlations for closures, which causes considerable uncertainties in their results. Thus, well-defined experimental data for local boiling parameters are essential for the development and validation of the wall boiling constitutive models. This paper presents new experimental data on the local bubble parameters and the wall temperatures along the heated tube for the subcooled flow boiling under high-pressure conditions. The radial distributions of the bubble parameters, namely, void fraction, bubble velocity, interfacial area concentration, and Sauter mean diameter were measured at multiple elevations to evaluate their development along the flow. Furthermore, the experimental data set was utilized to validate physical models for predicting subcooled flow boiling using a CMFD code. The source of discrepancies between the experimental and calculated results were analyzed and possible directions for research in subcooled flow boiling under high-pressure conditions were defined.

Sensitivity study of momentum and turbulence models for subcooled boiling phenomena simulation

This sensitivity analysis of the momentum and turbulence equations uses the Eulerian two-phase approach and intends to achieve a validated modeling for subcooled boiling flows. The studied regime is relevant to many industry applications and to the critical heat flux phenomenon, an important process for design and safety analyses of water-cooled nuclear power plants. Ascending water flows in heated circular pipes are modeled under subcooled boiling condition and applying a combination of computational multi-fluid dynamics (CMFD) models, each one for the estimation of specific terms of the governing equations. Turbulence closure, drag, lift, turbulent interaction, turbulent dispersion, wall lubrication and interfacial area models are investigated through variations around a reference model set defined based on the literature review, changing each model one at a time to study their impacts on the simulation results. Key parameters, such as void fraction and temperature profiles, are chosen for the evaluation of the results. Despite the difficulty of tracking the contributions of simultaneously applied models, the Legendre–Magnaudet lift force and the Burns et al. turbulent dispersion force models show good agreement with the experimental data of a flow at 4.5 MPa used for the quality verification of the simulations. These models are also applied for flows with pressures ranging from 1.5 to 15 MPa, and they lead to promising results. This study gives interesting insights on the influence of the distinct models composing momentum and turbulence calculations, contributing to the validation effort of the CMFD approach for subcooled boiling flows.

Numerical analysis of pre-dryout sequences through the route of interfacial evolution in annular gas-liquid two-phase flow with phase change

Numerical modeling of two-phase annular flow boiling has been carried out inside a tube using volume of fluid based computational multifluid dynamics. The proposed numerical methodology has been validated with available experimental results from literature. The stages of bubble nucleation, growth, merging, bursting, droplet entrainment, film rewetting, and dryout has been clearly visualized for diabatic annular mist flow. Plots of liquid phase fraction and average heat transfer coefficient were plotted which shows decreasing trends with axial space. Effect of different degrees of superheats and gas-liquid velocities at a higher working pressure of 40 bar have been studied, which can be commonly observed in boiling water reactor (BWR) conditions. Dryout is found to happen early in the axial length if the degree of superheat and flow velocities increases. The chaotic interfacial behavior has been analyzed with mean, standard deviation and attractor plot of space time-varying values of liquid phase fraction.

Void-fraction measurement with high spatial resolution in a 5×5 rod bundle by linear-accelerator-driven X-ray computed tomography over a wide pressure range

Void fraction (i.e., the volume fraction occupied by gas) is a key parameter for determining the coolability and neutron-moderating performance of a water-cooled nuclear reactor. To develop computational multi-fluid dynamics models for determining the void-fraction distribution, experimental data of comparable quality are required. We have developed a high-energy X-ray computed tomography (CT) system to acquire three-dimensional void-fraction distributions. The CT system comprises a linear-accelerator-driven high-energy X-ray source and a linear detector array. We quantified a boiling two-phase flow in a 5 × 5 heated rod bundle at high pressure, simulating a fuel-rod bundle in a boiling water reactor (BWR). Because the axial travel of the CT system is 4 m and includes the entire BWR fuel-rod bundle, we optimized the CT imaging conditions and reconstruction method for rod-bundle visualization to reduce uncertainties due to density fluctuations in the boiling flow and imaging artifacts. We conducted a boiling experiment at a low flow rate and low thermal power and acquired three-dimensional distributions of the void fraction over a wide pressure range of 0.1–7.2 MPa. The experiment provided three-dimensional void-fraction distributions with high spatial resolution, especially in subchannel regions surrounded by rods, and the results are suitable for validating three-dimensional thermal-hydraulic analysis codes.

Nuclear Safety and Thermal Hydraulics: Personal Thoughts and Some Recent Progress

An attempt is made in the first part of this paper to review the history of reactor safety and draw conclusions about trends that could be avoided and directions that could lead to robust reactor designs that would not be susceptible to severe accidents. In the second part, progress in reactor thermal hydraulics is observed by reviewing the list of conference sessions. Finally, a report is made on some recent work on two computational problems: the prediction of departure from nucleate boiling and the potential spatial coupling of computational multifluid dynamics methods to achieve multiscale, high-resolution simulations.

On dual-grid level-set method for contact line modeling during impact of a droplet on hydrophobic and superhydrophobic surfaces

In this paper, a numerical methodology for modeling contact line motion in a dual-grid level-set method (DGLSM) – solved on a uniform grid for interface which is twice that for the flow equations – is presented. A quasi-dynamic contact angle model – based on experimental inputs – is implemented to model the dynamic wetting of a droplet, impacting on a hydrophobic or a superhydrophobic surface. High-speed visualization experiments are also presented for the impact of a water droplet on hydrophobic surfaces, with non-bouncing at smaller and bouncing at larger impact velocity. The experimental results for temporal variation of the droplet shapes, wetted-diameter and maximum height of the droplet match very well with the DGLSM based numerical results. The validation of the numerical results is also presented with already published experimental results, for the non-bouncing on a hydrophobic and bouncing on a superhydrophobic surface, at a constant impact velocity. Finally, a qualitative as well as quantitative performance of the DGLSM as compared to the traditional level set method (LSM) is presented by considering our experimental results. The accuracy of the partially refined DGLSM is close to that of the fine-grid based LSM, at a computation cost which is close to that of the coarse-grid based LSM. The DGLSM is demonstrated as an improved LSM for the computational multi-fluid dynamics (CMFD) simulations involving contact line motion.

Computational multi-fluid dynamics predictions of critical heat flux in boiling flow

Extensive efforts have been made in the last five decades to evaluate the boiling heat transfer coefficient and the critical heat flux in particular. Boiling crisis remains a major limiting phenomenon for the analysis of operation and safety of both nuclear reactors and conventional thermal power systems. As a consequence, models dedicated to boiling flows have being improved. For example, Reynolds Stress Transport Model, polydispersion and two-phase flow wall law have been recently implemented. In a previous work, we have evaluated computational fluid dynamics results against single-phase liquid water tests equipped with a mixing vane and against two-phase boiling cases. The objective of this paper is to propose a new mechanistic model in a computational multi-fluid dynamics tool leading to wall temperature excursion and onset of boiling crisis. Critical heat flux is calculated against 150 tests and the mean relative error between calculations and experimental values is equal to 8.3%. The model tested covers a large physics scope in terms of mass flux, pressure, quality and channel diameter. Water and R12 refrigerant fluid are considered. Furthermore, it was found that the sensitivity to the grid refinement was acceptable.

Level set method for computational multi-fluid dynamics: A review on developments, applications and analysis

Functions and conservation as well as subsidiary equations in Level Set Method (LSM) are presented. After the mathematical formulation, improvements in the numerical methodology for LSM are reviewed here for advection schemes, reinitialization methods, hybrid methods, adaptive-grid LSM, dual-resolution LSM, sharp-interface LSM, conservative LSM, parallel computing and extension from two to multi fluid/phase as well as to various types of two-phase flow. In the second part of this article, LSM method based Computational Multi-Fluid Dynamics (CMFD) applications and analysis are reviewed for four different types of multi-phase flow: separated and parallel internal flow, drop/bubble dynamics during jet break-up, drop impact dynamics on a solid or liquid surface and boiling. In the last twenty years, LSM has established itself as a method which is easy to program and is accurate as well as computationally-efficient.

CMFD and the critical-heat-flux grand challenge in nuclear thermal–hydraulics – A letter to the Editor of this special issue

After very many rather naïve attempts to understand and model Critical Heat Flux (CHF) on the basis of unique mechanisms that resulted in a myriad models and of correlations, we came “back” to Look Up Tables that implicitly recognize that the data are not correlatable in general ways and then, with the advent of Computational Multi-Fluid Dynamics (CMFD) methods back again to predicting CHF mechanistically. The situation is clearly much more complicated in the fuel rod bundle assemblies used in nuclear reactors than in tubes or other simple channel geometries. For rod bundles, subchannel analysis methods have been used but the challenge of correlating CHF to the local conditions remains, in addition to the difficulties in computing the inter-subchannel fluxes.Recently, CMFD computations of the critical heat flux became the grand challenge and efforts were undertaken on both sides of the Atlantic to produce predictions of CHF for both the Departure from Nucleate Boiling (DNB) and the Dryout situations in PWRs and BWRs, respectively. CMFD methods come closer to tackling in a “natural” way the fuel-bundle and transient problems also, as the same basic, microscopic-level models and numerical techniques can be applied to any geometry also under transient conditions if sufficient computational resources are available. Much more advanced instrumentation is in the meantime producing the much more detailed, microscopic data needed to validate the CMFD methods.The paper reviews briefly the historical developments and then focuses on the recent CMFD work, its promises and still existing restrictions; the phenomena are too complex to be fully resolved by CMFD. Although we had set this as a goal over ten years ago, we are not there yet, but the spinoffs from this effort have been beneficial.

CMFD 코드의 난류 모델 및 비견인력 모델의 검증 계산

The standard drag force and virtual mass force, which exert to the primary flow direction, are generally considered in two-phase analysis computational codes. In this paper, the lift force, wall lubrication force, and turbulent dispersion force including turbulence models, which are essential for a computational multi-fluid dynamics model and play an important role in motion perpendicular to the primary flow direction, were introduced and verified with conceptual problems.

Progress in computational microfluidics using TransAT

The paper reports on the progress made in predicting single- and multi-phase microfluidics flows using the computational multi-fluid flow dynamics (CMFD) code TransAT. In the multi-phase context, the code uses either the level-set approach or the phase-field variant as the “Interface Tracking Methods”. The solver incorporates phase-change capabilities, triple-line dynamics models, Marangoni effects, electro-wetting and a micro-film sub-grid scale model for lubrication. Subtle microfluidics problems like droplet generation or surface tension-driven flows are shown to be within reach of modern CMFD techniques using interface tracking, with relatively fast CPU response times. In most of the cases presented here, the comparison between CMFD and experiments is rather satisfactory.

Numerical simulation of species transfer across fluid interfaces in free-surface flows using OpenFOAM

This paper presents the Continuous-Species-Transfer (CST) method, which enables interface capturing techniques – a group among Computational Multi-Fluid Dynamics (CMFD) methods that rely upon a smooth interface representation – to deal with species transfer. In this study we examine realistic species transfer across fluid interfaces, taking into account both the steep interfacial concentration gradients (at high Schmidt numbers) and the sharp interfacial concentration jump (at high Henry coefficients due to different species solubilities). Thus, the main objective is to establish the CST method for species transfer across fluid interfaces of arbitrary morphology in free-surface flows at high viscosity and density ratios.Detailed numerical simulations of single rising bubbles have been performed at high resolutions. Results were compared to experimental data and correlations derived thereof.

TWO-PHASE CFD: THE VARIOUS APPROACHES AND THEIR APPLICABILITY TO EACH FLOW REGIME

Two-phase Computational Fluid Dynamics (CFD) or CMFD (Computational Multi-Fluid Dynamics) is being applied to some nuclear reactor thermalhydraulic investigations. The NURESIM and NURISP projects of the European 5th and 6th Framework programs made some pioneering efforts to start some applications to a few selected reactor issues such as the Critical Heat Flux or the Pressurized Thermal shock. The extreme variety of flow configurations in steam-water two-phase flow makes the modeling issue very complex. Myriads of model options are available in the vast domain of CMFD, with various treatments of turbulence and of interfaces; the methods for choosing model options depending on the application have to be clarified. The purpose of this paper is to list and classify model options, to discuss some conditions and limits of applicability of the various options, and to identify the modeling needs for closure of the system of equations. The proposed classification of the modeling approaches is based on the space and time filtering or averaging of basic equations and on the number of phases and fields that are distinguished. The various flow processes that must be modeled by closure relations are identified for each type of approach. The applicability of each of these methods to each flow regime is defined and the present degree of maturity of the models is evaluated. Considering only Eulerian approaches used in an open medium, it is shown that five main approaches are considered: the RANS approach, the pseudo-DNS approach, and three types of space-filtered methods. Some of these methods can be applied only to a reduced number of flow regimes. Attention is drawn on the need to specify the model options, to guaranty the consistency between options, and to ensure completeness of closure terms. © 2011 by Begell House, Inc.

Computational heat transfer and two-phase flow topology in miniature tubes

Detailed computational multi-fluid dynamics simulations have been performed to study the effect of two-phase flow regime on heat transfer in small diameter pipes. Overall the heat removal rate in two-phase flow is higher than in single phase. Subtle differences in thermal removal rates are revealed when the flow-regime transitions from bubbly to slug and slug-train configurations. It is found that the wall thermal layer is affected by two separate mechanisms: an early-stage compression due to gas-jet fragmentation into slugs or bubbles, and a background inclusion-induced flow superimposed on the equivalent single-phase fully developed flow far downstream. The first mechanism resembles a confinement or blockage effect, and is shown to directly influence radial temperature gradients. The downstream mechanism is a cell-based developed flow (rather than fully developed), and is shown here to increase the wall shear in the vicinity of the cell, leading to higher heat transfer rates. The mean Nusselt number distribution shows that the bubbly, slug and slug-train patterns transport as much as three to four times more heat from the tube wall to the bulk flow than pure water flow. A mechanistic heat transfer model is proposed, based on frequency and length scale of inclusions.