Closure Model Research Articles

Modelling of high-velocity free-surface flows: a revised interfacial area approach

The specific interface area transport equation is derived from first principles, and a closure model for turbulent flow is proposed. The flow is modelled by a two-phase method providing velocities of both phases at the bubbly, spray and the intermediate large scale interface (LSI) regimes. The interface area is transported by the interface velocity – a linear combination of corresponding phase velocities and a turbulent drift velocity. The resulting equation includes the source terms due to the bubble (droplet) breakup and coalescence, and turbulent splashes at the interface. A model is proposed for the source term in the LSI regime. The model is implemented in the developer's version of the Simcenter STAR-CCM+ ® CFD code. The new model is applied to self-aerating water flows down stepped chutes; the results are in reasonable agreement with the experimental data.

Direct calculation of the eddy viscosity operator in turbulent channel flow at Re τ = 180

This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method (Mani & Park, Phys. Rev. Fluids, 2021, 054607) to direct numerical simulation (DNS) of a turbulent channel flow at $Re_\tau =180$ using two different forcing strategies that are designed to separately assess the anisotropy and non-locality of momentum mixing. In the first strategy, the leading term of the Kramers–Moyal expansion of the eddy viscosity is quantified, revealing all 81 tensorial coefficients that essentially characterise the local-limit eddy viscosity. The results indicate the following: (1) the eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both the mean strain rate and mean rotation rate tensors associated with the momentum field and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity is quantified as an integration kernel revealing the non-local influence of the mean momentum gradient at each wall-normal coordinate on all nine components of the Reynolds stresses over the channel width. Our results indicate that while the shear component of the Reynolds stress is reasonably reproduced by the local mean gradients, other components of the Reynolds stress are highly non-local. These results provide an understanding of anisotropy and non-locality requirements for closure modelling of momentum transport in attached wall-bounded turbulent flows.

A Computational Model Reveals How Varying Muscle Activation in the Lateral Pharyngeal Wall and Soft Palate Differentiates Velopharyngeal Closure Patterns.

Finite element (FE) models have emerged as a powerful method to study biomechanical complexities of velopharyngeal (VP) function. However, existing models have overlooked the active contributions of the lateral pharyngeal wall (LPW) in VP closure. This study aimed to develop and validate a more comprehensive FE model of VP closure to include the superior pharyngeal constrictor (SPC) muscle within the LPW as an active component of VP closure. The geometry of the velum and the lateral and posterior pharyngeal walls with biomechanical activation governed by the levator veli palatini (LVP) and SPC muscles were incorporated into an FE model of VP closure. Differing muscle activations were employed to identify the impact of anatomic contributions from the SPC muscle, LVP muscle, and/or velum for achieving VP closure. The model was validated against normative magnetic resonance imaging data at rest and during speech production. A highly accurate and validated biomechanical model of VP function was developed. Differing combinations and activation of muscles within the LPW and velum provided insight into the relationship between muscle activation and closure patterns, with objective quantification of anatomic change necessary to achieve VP closure. This model is the first to include the anatomic properties and active contributions of the LPW and SPC muscle for achieving VP closure. Now validated, this method can be utilized to build robust, comprehensive models to understand VP dysfunction. This represents an important advancement in patient-specific modeling of VP function and provides a foundation to support development of computational tools to meet clinical demand.

Neural differentiable modeling with diffusion-based super-resolution for two-dimensional spatiotemporal turbulence

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.

Numerical simulation on the influence of artificial island on reef hydrodynamics

The construction of artificial island can greatly change the reef hydrodynamics, leading to increased water level and wave height as well as changes in flow field distribution. These alterations can affect sediment transport on the reef, and increase the risk of overtopping and structure instability. A numerical model based on the Reynolds Averaged Navier-Stokes (RANS) equations and k-ε turbulence closure model was developed to investigate the influence of artificial island on reef hydrodynamics. The numerical model was validated against the experimental results of wave height, mean water level, and wave breaking morphology. Detailed flow field, wave height, and wave set-up in front of artificial island were further analyzed based on the validated model. After building the reef-top structure, the wave breaking and offshore currents at reef edge were amplified. The flow stratification and increase of the wave set-up were also found on the reef flat. Furthermore, we found the relationship between maximum flow velocities on the reef flat and incoming wave conditions could be characterized by two non-dimensional parameters: |u¯|max/g(η¯+hr), (η¯+hr)/Hi.

Crack Growth Analytical Model Considering the Crack Growth Resistance Parameter Due to the Unloading Process

Crack growth analysis is essential for probabilistic damage tolerance assessment of aeroengine life-limited parts. Traditional crack growth models directly establish the stress ratio–crack growth rate or crack opening stress relationship and focus less on changes in the crack tip stress field and its influence, so the resolution and accuracy of maneuvering flight load spectral analysis are limited. To improve the accuracy and convenience of analysis, a parameter considering the effect of unloading amount on crack propagation resistance is proposed, and the corresponding analytical model is established. The corresponding process for acquiring the model parameters through the constant amplitude test data of a Ti-6AL-4V compact tension specimen is presented. Six kinds of flight load spectra with inserted load pairs with different stress ratios and repetition times are tested to verify the accuracy of the proposed model. All the deviations between the proposed model and test life results are less than 10%, which demonstrates the superiority of the proposed model over the crack closure and Walker-based models in addressing relevant loading spectra. The proposed analytical model provides new insights for the safety of aeroengine life-limited parts.

A semi-analytical transient undisturbed velocity correction scheme for wall-bounded two-way coupled Euler-Lagrange simulations

Force closure models employed in Euler-Lagrange (EL) point-particle simulations rely on the accurate estimation of the undisturbed fluid velocity at the particle center to evaluate the fluid forces on each particle. Due to the self-induced velocity disturbance of the particle in the fluid, two-way coupled EL simulations only have access to the disturbed velocity. The undisturbed velocity can be recovered if the particle-generated disturbance is estimated. In the present paper, we model the velocity disturbance generated by a regularized forcing near a planar wall, which, along with the temporal nature of the forcing, provides an estimate of the unsteady velocity disturbance of the particle near a planar wall. We use the analytical solution for a singular in-time transient Stokeslet near a planar wall (Felderhof [1]) and derive the corresponding time-persistent Stokeslets. The velocity disturbance due to a regularized forcing is then obtained numerically via a discrete convolution with the regularization kernel. The resulting Green's functions for parallel and perpendicular regularized forcing to the wall are stored as pre-computed temporal correction maps. By storing the time-dependent particle force on the fluid as fictitious particles, we estimate the unsteady velocity disturbance generated by the particle as a scalar product between the stored forces and the pre-computed Green's functions. Since the model depends on the analytical Green's function solution of the singular Stokeslet near a planar wall, the obtained velocity disturbance exactly satisfies the no-slip condition and does not require any fitted parameters to account for the rapid decay of the disturbance near the wall. The numerical evaluation of the convolution integral makes the present method suitable for arbitrary regularization kernels. Additionally, the generation of parallel and perpendicular correction maps enables to estimate the velocity disturbance due to particle motion in arbitrary directions relative to the local flow. The convergence of the method is studied on a fixed particle near a planar wall, and verification tests are performed in the Stokes regime on a settling particle parallel to a wall and a free-falling particle perpendicular to the wall.

Tectonic evolution of the early Paleozoic intraplate orogen in the South China Block: Insights from Ductile Shear Zones in North Wuyishan

The ductile shear zones within the North Wuyishan domain are key to understand the tectonic evolution of the South China Block (SCB). This study integrates a multifaceted approach, including field observations, thin section analysis, quartz electron backscatter diffraction (EBSD), zircon U-Pb dating, and mica 40Ar/39Ar dating, to elucidate the deformation history of these shear zones in North Wuyishan. The research identifies a two-stage deformation process of early Paleozoic. The initial D1 phase is marked by a top-to-SW thrusting shear, with associated felsic veins dated to the Ordovician period (447 ± 10 Ma to 459 ± 4 Ma), correlating with high-grade metamorphism and partial melting. The later D2 phase is characterized by NE-striking foliation and lineation, indicative of sinistral strike-slip shear, dated to the early Devonian (412 Ma) and early Carboniferous (∼354 Ma). The D1 phase suggests early crustal thickening and melting within the Cathaysia block, while D2 indicates a transpressional regime during post-orogenic adjustment. The geological features of the SCB, notably the absence of arc magmatism, ophiolitic mélange, and high-pressure metamorphism, comply with an intracontinental rift closure model as previously proposed. This model supports the hypothesis that the Early Paleozoic intracontinental orogeny in the SCB was likely a far-field consequence of a continental collision between the SCB-North Vietnam and South Vietnam blocks near the east Gondwana supercontinent.

Experimental Study of Turbulent Premixed Flames of Gas-to-Liquids (GTL) Fuel in a Fan-Stirred Combustion Bomb

This study experimentally investigates the turbulent flame speeds (St) of Gas-to-Liquids (GTL) fuel and a 50/50 blend with diesel across turbulence intensities (u') ranging from 0.5 to 3.0 m/s and equivalence ratios (Φ) from 0.7 to 1.3. Experiments were conducted using a cylindrical fan-stirred combustion bomb at an initial temperature (Ti) of 463 K and atmospheric pressure under near homogeneous and isotropic turbulence (HIT) conditions. A pressure transducer measured the St of the propagating GTL flame. High-speed imaging reveals that changes in flame brightness are associated with variations in flame temperature and soot incandescence. Compared to diesel, stoichiometric GTL and the 50/50 diesel-GTL blend showed peak combustion pressure reductions of 8.9% and 4.9%, respectively. Rich diesel fuel and lean GTL exhibited higher pressure rise rates, flame propagation, and St due to their Lewis numbers (Le) being less than one, enhancing flame-turbulence interaction. At u` of 0.5, 1.5, and 3.0 m/s, St for GTL increased by approximately 3.6%, 5.3%, and 2.8%, respectively, when compared to diesel, with these increases observed at Φ < 1.1. Transition from wrinkled to corrugated flamelets with increasing u` supports models predicting flame stability and potential industrial combustion efficiency improvements. Comparisons with numerical St results using the Zimont Turbulent Flame Speed Closure (Zimont TFC) model showed good agreement at lower (u' = 0.5 m/s) and mid-range (u' = 2.0 m/s) turbulence intensities but discrepancies at higher intensities (u' = 3.0 m/s), highlighting the need to refine numerical models for more accurate predictions across all turbulence levels.

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

Generalized field inversion strategies for data-driven turbulence closure modeling

Most data-driven turbulence closures are based on the general structure of nonlinear eddy viscosity models. Although this structure can be embedded into the machine learning algorithm and the Reynolds stress tensor itself can be fit as a function of scalar- and tensor-valued inputs, there exists an alternative two-step approach. First, the spatial distributions of the optimal closure coefficients are computed by solving an inverse problem. Subsequently, these are expressed as functions of solely scalar-valued invariants of the flow field by virtue of an arbitrary regression algorithm. In this paper, we present two general inversion strategies that overcome the limitation of being applicable only when all closure tensors are linearly independent. We propose to either cast the inversion into a constrained and regularized optimization problem or project the anisotropy tensor onto a set of previously orthogonalized closure tensors. Using the two-step approach together with either of these strategies then enables us to quantify the model-form error associated with the closure structure independent of a particular regression algorithm. Eventually, this allows for the selection of the a priori optimal set of closure tensors for a given, arbitrary complex test case.

Hydrodynamic force coefficients for spherical triangle shell fragments: Dependence on the aspect ratio and flatness

Euler–Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces for individual particles. Our goal is to develop models that can prescribe these forces for arbitrarily orientated shell objects. Here, we use computational fluid dynamics simulations of steady bottom-boundary layer flow over a series of spherical triangle shell fragments to calculate the hydrodynamic forces. The simulations explicitly resolve the wall boundary layers using grid resolution on the order of y+=1 at the shell fragment surface and use the SST k-omega turbulence closure model. These fragments cover a range of aspect ratio and flatness characteristics. The shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while characteristic length of the fragment is held constant to define the overall fragment size. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.

Response of Upper Ocean to Parameterized Schemes of Wave Breaking under Typhoon Condition

The study of upper ocean mixing processes, including their dynamics and thermodynamics, has been a primary focus for oceanographers and meteorologists. Wave breaking in deep water is believed to play a significant role in these processes, affecting air–sea interactions and contributing to the energy dissipation of surface waves. This, in turn, enhances the transfer of gas, heat, and mass at the ocean surface. In this paper, we use the FVCOM-SWAVE coupled wave and current model, which is based on the MY-2.5 turbulent closure model, to examine the response of upper ocean turbulent kinetic energy (TKE) and temperature to various wave breaking parametric schemes. We propose a new parametric scheme for wave breaking energy at the sea surface, which is based on the correlation between breaking wave parameter RB and whitecap coverage. The impact of this new wave breaking parametric scheme on the upper ocean under typhoon conditions is analyzed by comparing it with the original parametric scheme that is primarily influenced by wave age. The wave field simulated by SWAVE was verified using Jason-3 satellite altimeter data, confirming the effectiveness of the simulation. The simulation results for upper ocean temperature were also validated using OISST data and Argo float observational data. Our findings indicate that, under the influence of Typhoon Nanmadol, both parametric schemes can transfer the energy of sea surface wave breaking into the seawater. The new wave breaking parameter RB scheme effectively enhances turbulent mixing at the ocean surface, leading to a decrease in sea surface temperature (SST) and an increase in mixed layer depth (MLD). This further improves upon the issue of uneven mixing of seawater at the air–sea interface in the MY-2.5 turbulent closure model. However, it is important to note that wave breaking under typhoon conditions is only one aspect of wave impact on ocean disturbances. Therefore, further research is needed to fully understand the impact of waves on upper ocean mixing, including the consideration of other wave mechanisms.

Numerical investigation of premixed syngas/air flame evolution in a closed duct with tulip flame formation

In this study, the dynamic behavior of the premixed syngas/air flames in enclosed ducts with obstacles at the blockage ratio of 0.5, as well as without obstacles, was studied via large eddy simulation and the turbulent flame speed closure model. The hydrogen volume fraction (hydrogen content in fuel) was set to 50 %. Results indicate that the simulation reproduced the flame shapes, flame speed and explosion overpressure observed in the experiments. In cases without obstacles, a “tulip” flame with a tulip cusp can be seen, and secondary cusps emerge on tulip lips due to the high-pressure zone ahead of “tulip” flame lips, leading to in a distorted “tulip” flame. In cases with obstacles, the flame develops hemispherical and finger shapes upstream of the obstacles and evolves into a “tulip” flame downstream of the obstacles due to vortices and adverse pressure gradients. The alteration of the flow direction within the unburned and burned zones results in intricate flame shapes. Flame speed and overpressure show a close relationship and exhibit oscillations following the generation of the “tulip” flame. Typically, the velocity, pressure and flow fields adjacent to the flame front can affect dynamic behaviors of premixed syngas/air flames.

Building-block-flow computational model for large-eddy simulation of external aerodynamic applications

Computational fluid dynamics is an essential tool for accelerating the discovery and adoption of transformative designs across multiple engineering disciplines. Despite its many successes, no single approach consistently achieves high accuracy for all flow phenomena of interest, primarily due to limitations in the modeling assumptions. Here, we introduce a closure model for wall-modeled large-eddy simulation to address this challenge. The model, referred to as the Building-block Flow Model (BFM), rests on the premise that a finite collection of simple flows encapsulates the essential missing physics necessary to predict more complex scenarios. The BFM is designed to: (1) predict multiple flow regimes, (2) unify the closure model at solid boundaries and the rest of the flow, (3) ensure consistency with numerical schemes and gridding strategies by accounting for numerical errors, (4) be directly applicable to arbitrary complex geometries, and (5) be scalable to model additional flow physics in the future. The BFM is utilized to predict key quantities in five cases, including an aircraft in landing configuration, demonstrating similar or superior capabilities compared to previous state-of-the-art models. The design of BFM opens up new opportunities for developing closure models that can accurately represent various flow physics across different scenarios.

Characteristics of Deterministic and Stochastic Unsteadiness of Trailing Edge Cutback Film Cooling Flows

Abstract Trailing edge cutback film cooling flows are ubiquitous in small and medium gas turbines, but they are difficult to predict accurately due to the inherent deterministic and stochastic unsteadiness that controls the effectiveness of the cooling system. To help develop accurate closure models for such flows, the characteristics of both types of unsteadiness and their effects on the mean flows are analyzed in this research. Zonal detached eddy simulation (ZDES) is performed on a trailing edge cutback flow model, and the numerical results are validated against the measured data. Then, by using spectral proper orthogonal decomposition (SPOD) reconstruction, the original dataset is segregated into deterministic and stochastic unsteadiness. The characteristics of the stress tensor and the heat flux of each type of unsteadiness are analyzed in detail, and notable differences between the two unsteadiness are identified in terms of the stress tensor anisotropy and distribution of unsteady kinetic energy and heat flux. By propagating the unsteadiness through the Reynolds-averaged Navier–Stokes (RANS) equations, the effect of different unsteadiness on the mean flow prediction is quantified. An accurate prediction of the total stress tensor reduces the prediction error in the velocity field by 79% and cooling effectiveness by 55%. An accurate prediction of the total heat flux vector reduces the prediction error in cooling effectiveness further by 37%. These findings provide valuable knowledge for the physical understanding, turbulence modeling, and aerothermal design of cutback trailing edge flows.

Large/small eddy simulations: A high-fidelity method for studying high-Reynolds number turbulent flows

Direct numerical simulations (DNS) are one of the main ab initio tools to study turbulent flows. However, due to their considerable computational cost, DNS are primarily restricted to canonical flows at moderate Reynolds numbers, in which turbulence is isolated from the realistic, large-scale flow dynamics. In contrast, lower fidelity techniques, such as large eddy simulations (LES), are employed for modeling real-life systems. Such approaches rely on closure models that make multiple assumptions, including turbulent equilibrium, small-scale universality, etc., which require prior knowledge of the flow and can be violated. We propose a method, which couples a lower-fidelity, unresolved, time-dependent calculation of an entire system (LES) with an embedded small eddy simulation (SES) that provides a high-fidelity, fully resolved solution in a sub-region of interest of the LES. Such coupling is achieved by continuous replacement of the large SES scales with a low-pass filtered LES velocity field. The method is formulated in physical space, with no assumptions of equilibrium, small-scale structure, and boundary conditions. A priori tests of both steady and unsteady homogeneous, isotropic turbulences are used to demonstrate the method's accuracy in recovering turbulence properties, including spectra, probability density functions of the intermittent quantities, and sub-grid dissipation. Finally, SES is compared with two alternative approaches: one embedding a high-resolution region through static mesh refinement and a generalization of the traditional volumetric spectral forcing. Unlike these methods, SES is shown to achieve DNS-level accuracy at a fraction of the cost of the full DNS, thus opening the possibility to study high-Re flows.

Making cups and rings: the 'stalled-wave' model for macropinocytosis.

Macropinocytosis is a broadly conserved endocytic process discovered nearly 100 years ago, yet still poorly understood. It is prominent in cancer cell feeding, immune surveillance, uptake of RNA vaccines and as an invasion route for pathogens. Macropinocytic cells extend large cups or flaps from their plasma membrane to engulf droplets of medium and trap them in micron-sized vesicles. Here they are digested and the products absorbed. A major problem - discussed here - is to understand how cups are shaped and closed. Recently, lattice light-sheet microscopy has given a detailed description of this process in Dictyostelium amoebae, leading to the 'stalled-wave' model for cup formation and closure. This is based on membrane domains of PIP3 and active Ras and Rac that occupy the inner face of macropinocytic cups and are readily visible with suitable reporters. These domains attract activators of dendritic actin polymerization to their periphery, creating a ring of protrusive F-actin around themselves, thus shaping the walls of the cup. As domains grow, they drive a wave of actin polymerization across the plasma membrane that expands the cup. When domains stall, continued actin polymerization under the membrane, combined with increasing membrane tension in the cup, drives closure at lip or base. Modelling supports the feasibility of this scheme. No specialist coat proteins or contractile activities are required to shape and close cups: rings of actin polymerization formed around PIP3 domains that expand and stall seem sufficient. This scheme may be widely applicable and begs many biochemical questions.

Experimental and CFD studies on collection efficiency of separator with arc settlers of fluidized bed catalytic reactor

Separation of catalyst dust from gas in a fluidized bed reactor is an important process. A new solid-gas separator with arc settlers was developed, in which a stable wave flow pattern of the dusty gas flow is formed. The model was based on the RANS approach using the Reynolds Stress Model for the turbulence closure and the Discrete Phase Model. Validating the simulation results with the test data showed good convergence, no more than 6% in the pressure drop and less than 15.5% in collection efficiency at different inlet gas velocities. The CFD study revealed that with a dusty gas inlet velocity of no more than 1 m/s and a catalyst particle larger than 20 μm, efficiency close to 100% is achieved with a pressure drop of less than 60 Pa. Maximum efficiency is achieved when the number of rows of the arc settlers with 40 mm diameter is 8.

Investigation of Wall Boiling Closure, Momentum Closure and Population Balance Models for Refrigerant Gas–Liquid Subcooled Boiling Flow in a Vertical Pipe Using a Two-Fluid Eulerian CFD Model

The precise design of heat exchangers in automobile air conditioning systems for more sustainable electric vehicles requires an enhanced assessment of CFD mechanistic models for the subcooled boiling flow of pure eco-friendly refrigerant. Computational Multiphase Flow Dynamics (CMFDs) relies on two-phase closure models to accurately depict the complex physical phenomena involved in flow boiling. This paper thoroughly examines two-phase CMFD flow boiling, incorporating sensitivity analyses of critical parameters such as boiling closures, momentum closures, and population balance models. Three datasets from the DEBORA experiment, involving vertical pipes with subcooled boiling flow of refrigerant at three different pressures and varying levels of inlet liquid subcooling, are used for comparison with CFD simulations. This study integrates nucleate site density and bubble departure diameter models to enhance wall boiling model accuracy. It aims to investigate various interfacial forces and examines the S-Gamma and Adaptive Multiple Size-Group (A-MuSiG) size distribution methods for their roles in bubble break up and coalescence. These proposed approaches demonstrate their efficacy, contributing to a deeper understanding of flow boiling phenomena and the development of more accurate models. This investigation offers valuable insights into selecting the most appropriate sub-closure models for both boiling closure and momentum closure in simulating boiling flows.