Eulerian Two-phase Model Research Articles

Enhancing Natural Convection Heat Transfer Through Dome-Shaped Nanofluid Enclosures: Two-Phase Simulation Analysis

This study utilizes numerical analysis to investigate laminar flow and natural convective heat transfer of nanofluids (NFs) within dome-shaped enclosures (DSEs). The horizontal walls of the enclosure are adiabatic, while the vertical walls on the right and left are maintained at isothermal conditions with low and high temperatures, respectively. The study focuses on examining the impact of DSEs on flow patterns and natural convection (N.C.) under varying parameters, including Rayleigh numbers (Ra), Lewis numbers (Le), enclosure inclination angles, dome angles, and buoyancy ratio number (Nr). The Prandtl number (Pr) and nanoparticle volume fraction are consistently maintained at 10 and 0.05, respectively. The governing equations have been resolved by applying the Eulerian–Eulerian two-phase model. The study reveals that the DSE significantly influences flow dynamics, leading to smoother circulation patterns that intensify convection currents. This movement of hot fluid toward cooler regions within the enclosure enhances natural convective heat transfer. Across all enclosure inclination angles, the average Nusselt number (Nu) increases with higher Ra, while the Le remains constant at 4. Significantly, due to its robust convective currents, the average Nu in the DSE with a 45° dome angle surpasses those of corresponding square and rectangular enclosures.

Numerical study of uranium hexafluoride desublimation process based on Eulerian two-phase model

This paper presents a numerical study on the condensation process of uranium hexafluoride (UF6) in the supply and extraction system of a uranium enrichment plant. The numerical study was conducted using a standard UF6 receiving container with a nominal diameter of 127 mm and a volume of 8L under constant temperature boundary conditions. A phase change heat and mass transfer model for the desublimation process of uranium hexafluoride gas was established, and this model was combined with the Euler two fluid model to predict the distribution of key parameters such as temperature, pressure, and volume fraction of each phase during the UF6 cooling process, as well as the gas flow characteristics inside the container. In addition, this study also investigated the influence of various factors on the cooling rate. The research results indicated that UF6 gas initially condensed on the container wall and gradually diffused inward, with the highest solid density observed on the wall. Furthermore, increasing the inlet gas temperature, inlet mass flow rate, and reducing the cooling temperature, initial pressure inside the container could all enhance the desublimation rate to various degrees. The optimization plan proposed based on the above influencing factors could increase the yield of UF6 solid by 64.20% in 2 h, compared to the basic operating conditions.

Effects of the turbulent incoming flow condition on the wind–snow flow characteristics and accretion distribution in the cutting area of the high-speed railway

In addressing snowdrift disasters in high-speed railway cutting areas, this study utilized the improved delayed detached eddy simulation turbulence model, synthetic eddy method, and Eulerian two-phase flow model (Euler–Euler). Coupled with grid dynamic deformation techniques, the investigation facilitated extracting temporal variations in snow particle accumulation profiles within the cutting areas. The predicting accuracy of the numerical method was validated through the wind tunnel and wind–snow experimental data. Building upon this foundation, the study investigated how uniform and turbulent flow conditions impact snow distribution in the high-speed railway cutting areas. The analysis examined the turbulent flow structures, friction velocity distribution, and snow accretion contours within the cutting area. Findings indicate that the snow mass on the windward slope in the cutting area remains consistent under both flow conditions. However, there are significant differences in the rate of snow mass growth and the characteristics of snow accretion distribution. The disappearance of vortex structures at the base of the leeward slope is crucial for indicating the transition in the accumulation states of the surrounding snow particles. Under turbulent incoming flow conditions, the transition from large-scale vortex systems to vortex pairs on the leeward slope of the cutting is delayed, resulting in a postponed stable growth period for snow accretion. Additionally, strong erosion between the track bed and the leeward slope results in reduced snow accretion mass in these areas. In particular, at the simulation time of t = 150 min, under turbulent incoming flow conditions, the overall snow accumulation in the cutting decreased by 20.8% compared to the uniform incoming flow conditions. The snow mass in the leeward slope area decreased by 38.3%, and the track bed area experienced a 23.3% reduction in snow accumulation. In contrast, the snow quantity on the windward slope remained relatively consistent.

Investigating wave shape effect on sediment transport over migrating ripples using an eulerian two-phase model

A Reynolds-averaged two-phase Eulerian model for sediment transport, SedFoam, is utilized in a two-dimensional domain for a given sediment grain size, flow period, and mobility number to study the asymmetric and skewed flow effects on the sediment transport over coarse-sand migrating ripples. First, the model is validated with a full-scale water tunnel experiment of orbital ripple driven by acceleration skewed (asymmetric) oscillatory flow with good agreement in the flow velocity, net sediment transport, and ripple migration rate. The model results showed that the asymmetric flow causes a net onshore sediment transport of both suspended and near-bed load (the conventional bed load and part of the near-bed suspended load, responsible for ripple migration). The suspended load transport is driven by the “positive phase-lag” effect, while the near-bed transport is due to the large erosion of the boundary layer on the stoss flank, sediment avalanching on the lee flank, and the returning flux induced by the stoss vortex. Together, these processes result in a net onshore transport rate. In contrast, for an energetic velocity skewed (skewed) flow, the net transport rate is offshore directed. This is due to a larger offshore-directed suspended load transport rate, resulting from the “negative phase-lag” effect, compared to the onshore-directed near-bed load transport rate. Compared to the asymmetric flow, the onshore near-bed load transport (and migration) rate is limited by the larger offshore directed flux associated with returning flow on the lee side, due to a stronger lee vortex generation during the onshore flow half-cycle. In the combined asymmetric-skewed case, the near-bed load and migration rate are higher than in the asymmetric flow case. Moreover, the offshore-directed suspended load is much smaller compared to the skewed flow case due to a competition between the negative (due to velocity skewness) and positive (due to acceleration skewness) phase-lag effects. As a result, the net transport rate is onshore directed but slightly smaller than the asymmetric flow case.

Numerical investigation on critical heat flux for 5 × 5 fuel assemblies with a wide range of working conditions

To determine the safe boundary of fuel assembly operation and improve the heat transfer performance of fuel assembly, it is necessary to accurately calculate the thermohydraulic characteristics and the critical heat flux (CHF) in rod bundles. The Eulerian two-phase model coupled with extended wall boiling model was used to numerically investigate the 5 × 5 fuel rod bundle flows with four sets of mixing vane spacer grids. A wide range of working conditions were analyzed to validate the numerical method. The results indicate that the current numerical model can not only accurately calculate the CHF values but also predict the location of heat transfer crisis. Based on CFD (Computational Fluid Dynamics) results, the detailed two-phase flow distributions were provided to analyze the CHF performance under special structures, such as bowed rod and spacer backward shift. The quantitative results were obtained on the analyses of spacer position influence on CHF and the penalty effect of bowed rod. Furthermore, the prediction of present numerical model under low inlet subcooling conditions and cold rod CHF were discussed. The research of this paper provides support for the design and optimization of fuel assemblies.

Design Parameters Investigation on Sand Transportation Characteristics of V-Inclined Pipe Based on Eulerian–Eulerian Two-Phase Flow Model

During the operation of the water transportation pipelines in the upstream of the Yellow River, varying degrees of sand deposition often occur under a low flow rate. Taking into account the effect of different pipe inclinations, pipe diameters, and inlet sand content, the Eulerian–Eulerian two-phase model was applied in the numerical simulation of sediment-laden flow in a V-inclined pipe. The results indicate that there is a significant difference between a V-inclined pipe and horizontal pipe affected by gravity. Compared with the downward inclined pipe, sand deposition is evident in the upward inclined pipe. The high-velocity region moves upward and the asymmetry of the cross-sectional velocity increases. As the pipe diameter increases, the interaction between sand and the wall as well as the degree of turbulence decrease, so that the distribution of sand volume concentration across the cross section will be more uniform. Under different inlet sand content, the lowest point of the pipe experiences the most sand deposition, with sand volume concentration and velocity distribution across the cross-sections becoming uneven as inlet sand content increases. The location of the maximum liquid velocity varies from section to section. When the inlet sand content increases from 0.42% to 5%, the liquid velocity of the pipe cross-section no longer satisfies the rule of high velocity for middle and low velocity near the wall.

Investigation on the DNB-type critical heat flux in a fuel assembly with 5 by 5 rods

In this paper, Eulerian two-phase model coupled with wall boiling model was employed to simulate the departure from nucleate boiling (DNB) in a 5 × 5 fuel assembly. The numerical simulation accurately predicted the critical heat flux (CHF) and also its location. Compared with the calculated results from W-3 formula and FLICA subchannel code, the CFD (Computational Fluid Dynamics) calculations showed good agreement against experimental measurements with the deviation of 5%, but presented more detailed flow distribution. Based on CFD results, the method of CHF prediction was discussed with an eye on wall superheat, void fraction and vapor convective heat flux in rod surfaces. The distribution of flow field and liquid–vapor fraction affected by mixing vane were further studied. Mixing vane can continually influence the downstream thermal hydraulic characteristics, forming the diagonal circulation and square circulation with the flow development. As a result, the bubble aggregation firstly occurred on the surface of corner hot rod instead of central hot rod, which induced the local heat transfer crisis. The CFD calculations presenting the evolution process of physical parameters can provide guidance for rod bundle CHF test and fuel assembly design.

Numerical investigation on effects of fuel rod with different bow deformation ratio X on two-phase boiling and flow performances of coolant in fuel assembly

The bow deformation of fuel rod usually occurs in Pressurized Water Reactor (PWR). As the flow channel in fuel assembly changes due to the bowing, coolant in subchannels is redistributed, which influences flow and heat transfer performances of coolant. In this article, based on Eulerian two-phase model and RPI boiling model, a 3 × 3 fuel assembly with bow deformation is studied in the STAR-CCM+, and typical C-shape bow deformation happens to the center fuel rod. The effects of fuel rod with different bowing degrees on coolant two-phase boiling and flow performances are compared. Numerical model is verified by comparing with the experimental data. The results show that significant local boiling occurs in the bowing region and liquid phase temperature increases dramatically in subchannels where cross-sectional area decreases if bow deformation ratio X less than 0.5. The averaged void fraction in bowing region gradually increases with the bowing degree, and it increases dramatically if X less than 0.2. Besides, the axial position of the initial boiling is gradually advanced, and the area of high liquid phase heat transfer coefficient on the wall of bowing rod decreases sharply when X less than 0.4. Meanwhile, the cross flow reduces gradually with the increase of bowing degree, indicating that bow deformation will inhibit the generation of cross flow. The turbulent kinetic energy of coolant in the region with reduced cross-sectional area greatly decreases when X less than 0.2, and the inhomogeneity of distribution brings great challenge to the safe operation of nuclear reactor core. Besides, excessive bow deformation will cause a great pressure drop.

Effect of Mono-Dispersed Solids Slurry Characteristics on Horizontal Bends

Abstract: Erosion in multiphase flow due to the effect of solid particles is a key factor in wearing of industrial pipelines. In recent years, industries are using Computational Fluid Dynamics to study erosion wear in pipelines. Researchers have investigated various factors that affect the erosion of pipelines including particle size, velocity, coating material, fluid viscosity, region of pipe (bends/fittings convex or concave), etc. This paper investigates the effect of various slurry parameters on the rate of material erosion in the pipeline, under different sets of operation conditions. Silica sand (density= 2650 kg/m3 ) slurry was considered for the simulations, mixed in water at different volumetric concentration (12%, 24% and 36%), with an inlet velocity of 2.74 m/s and 3.56 m/s. The particle size was considered constant at 225µm, 450µm and 675µm, respectively. Simulations are done in ANSYS-FLUENT software under Eulerian two-phase model with k-ε approach. Results showed that the erosion rate followed the trend of increasing with an increase in all the above mentioned varying parameters as it varied from 8.25 mm/yr to 18.93 mm/yr. It was also hinted that as particle size reduced, the influence of velocity as a contributing parameter reduced which is explained by the fact that the mixture is leading from suspension state to colloidal state.

Computational Analysis of Erosion Wear Rate by Multiphase Flow in Optimum Bend Ratio of Pipeline

Abstract: Pipe bends are an integral part of transportation system as they help by providing flexibility in the path. In this paper, flow of mono-dispersed particles with carrier flow is simulated using Computational Fluid Dynamics by implementing Eulerian two-phase model in FLUENT. This paper is a forward stepping stone as it depicts the effect of pipeline bend on flow characteristic such as erosion rate, concentration profile, wall shear stress, etc. after numerous researches on pressure drop and velocity profiles. In this paper, a two-phase fluid of silica sand, having mean diameter of 450 µm (density = 2650 kg/m3 ), and water are mixed at the ratio of 8.82% solid concentration by weight and flown through a pipeline with diameter 53.0 mm and the optimum pipe bend ratio of 5.60 for minimum pressure loss.

Droplet Collection Efficiency Regularity of NACA0012 Airfoil Based on the Eulerian Method

Obtaining droplet collection efficiency (DCE) is vital for icing numerical simulations. A droplet impact model based on the Eulerian two-phase flow model was established in this work to analyze the influence of different incoming flow parameters on DCE. Then, the mathematical regularity of the DCE distribution was explored using the parametric description, and the functional relation of the regularity between the incoming condition and the DCE distribution was accomplished. The results showed that the calculated DCE of NACA0012 and the two-dimensional cylinder matched well with the test data. The incoming flow velocity and droplet size, rather than the liquid water content (LWC) of the incoming flow, affected the collection efficiency significantly. The DCE distribution under different conditions was normalized to the same mathematical form with the peak collection efficiency and maximum position. The mathematical form had a highly normal distribution, which was expressed with good regularity of the Reynolds number and droplet diameter. Regularity can greatly reduce the amount of calculation and improve the calculation accuracy, which plays a positive role in the numerical prediction of the icing problem.

Slurry flow characteristics through a horizontal pipeline at different Prandtl number

The settling behavior of solid particles in the slurry pipeline leads to bed formation and sedimentation at the bottom of the pipeline. This in turn causes the blockage of the pipeline resulting in more energy consumption and a pressure drop in the slurry pipeline. The present work investigates the effect of the different Prandtl numbers on the slurry flow characteristics through a horizontal pipe. Since the flow is a liquid-solid mixture, therefore, a steady-state three-dimensional Eulerian two-phase model in combination with the RNG k-ε turbulence model is implemented for the current simulation in the commercial software ANSYS FLUENT. Numerical predictions and procedures for the mixture of solid concentrations are generally in good agreement with the past experimental data available in the literature. Slurry flow features are examined at four different Prandtl numbers i.e., 2.88, 3.42, 4.62 and 5.83 for different-sized glass beads (125, 200, 275, 350 and 440 μm) slurry for the concentration ranging from 40 to 60% (by weight) at a mean flow-velocity of 5 m/s. The findings show that the pressure drop rises with the escalation in particle sizes and Prandtl number for chosen efflux concentration range. Furthermore, low Prandtl fluid demonstrates relatively higher granular pressure, temperature and wall shear stress, which further increases with raise in solid concentration and particle size. In addition, higher Prandtl number fluid demonstrates maximum specific energy consumption (SEC) for every particle and efflux concentration range. • 3D CFD modeling of slurry flow via horizontal straight pipe is investigated. • Effect of different Prandtl number on slurry flow characteristics is studied. • Effect of particle size and concentration on slurry pressure drop is presented. • At lower Prandtl number, maximum granular pressure and temperature is established. • Transportation of slurry with higher Prandtl fluid is more energy efficient.

Numerical Analysis of the Pulsating Heat Transfer of Ferrofluid in Helically Fluted Tubes

The flow and heat transfer characteristics in the corrugated tube mainly depend on flow parameters and geometric configurations of the tube, such as corrugated cross-section, corrugated angle, corrugated arrangement, corrugated pitch and depth, pulsating flow frequency, coolant types, and Reynolds number. This paper presents the pulsating thermal characteristics of ferrofluid flowing in the fluted tube using the de-ionized water and 0.015% by volume as working fluid flowing in the test section. Eulerian two-phase turbulence model validation has been performed in both steady and pulsating flow. The finite volume approach discretizes the Eulerian two-phase model. Numerical results indicate that the longitudinal and transverse secondary flows are induced differently via the pulsating flow. The heat transfer characteristics of pulsating fluid flow are significantly larger than that of continuous fluid flow. A higher pulsating frequency induces a heat transfer enhancement. However, pulsating flow increases pressure due to more flow complexity and rough augmentation. Due to the disturbed fluid flow and higher swirling motion, the heat transfer augmentation increases and corresponds with the published results.

Accuracy Assessment of the Eulerian Two-phase Model for the CFD Simulation of Gas Bubbles Dynamics in Alkaline Electrolyzers

To date, the most industrially developed technology to produce green hydrogen is represented by alkaline water electrolysis (AWE). To improve on design and efficiency of these devices, however, multiphysics simulations based on Computational Fluid Dynamics (CFD) are needed, able to account for electrophysical phenomena and multiphase flows. Focusing on internal flow optimization, the requirements for CFD simulations are anyhow extremely challenging, since solving the gas bubbles’ motion implies the solution of a two-phase flow characterized by very low Reynolds numbers and a high fraction of dispersed gas. Despite some interesting studies have been presented in the literature so far, validation of CFD results with detailed experimental measurements is quite rare and, therefore, the reliability of the adopted modelling approaches is not assessed yet. This study presents the results of a multivariate CFD analysis of an electrochemical cell and its validation through a literature test case. Bubbles generation is introduced as a source term, thus overlooking for the moment the electrochemistry to focus on fluid-dynamics. In particular, attention is given to the Eulerian multiphase modelling, investigating the influence of both the inter-phase interaction sub-models’ settings (e.g., lift and drag forces, virtual-mass force) and the general settings of the simulation. The mean velocity field of the PIV-measured bubbles is considered to assess the accuracy of numerical predictions, while the available high-definition flow pictures allow a qualitative assessment of the bubbles size and location. CFD results are shown to be in decent agreement with experimental data and able to reproduce the key flow features such as the spreading of the bubble curtains and the gas shifting towards the inner part of the cell. The effect of the bubbles’ diameter and of source layer thickness is also discussed.

A multi-dimensional two-phase mixture model for intense sediment transport in sheet flow and around pipeline

A two-phase mixture model is developed to simulate intense sediment transport covering the bed-load layer and suspended load layer. The proposed model maintains high accuracy as an Eulerian two-phase model but requires low computational cost. The proposed model applies an analytical formula for relative velocity between phases. The dense granular flow rheology is employed to close particle stress economically. The closure of Reynolds stress considers turbulence damping and small-scale fluctuation of fluid–particle interaction and particle collision. A damping function is adopted in eddy viscosity for extra turbulence damping from inter-particle interaction. The optimal exponent of the damping function refers to sediment shape and size. The sediment diffusion includes turbulence diffusion and shear-induced self-diffusion originating from dense sediment. The proposed model is validated by several sets of sheet flow cases (Shields number Θ = 0.44–2.20 and particle Reynolds number Res = 1.6–603.0) and shows a wide applicable range and good accuracy. The small-scale fluctuation and shear-induced self-diffusion improve the computation in the lower sheet flow layer where volumetric sediment concentration is larger than 0.2. Furthermore, the proposed model shows reasonable applicability on the multi-dimensional pipeline scour development. The scour profiles are well predicted and the Brier Skill Score = 0.809. However, the proposed model does not perform the wake characteristic around the pipeline sufficiently, and slight scour difference exists between the simulation and experiment.

Numerical simulation of early stages of scour around a submarine pipeline using a two-phase flow model

Current-induced scour around a submarine pipeline during onset and tunnel erosion are investigated in both clear-water and live-bed regimes using an Eulerian–Eulerian two-phase model for sediment transport. The Hybrid Fictitious Domain-Immersed Boundary (HFD-IB) method is adopted to simulate the pipeline structure. The model is validated against two published experimental data: (1) flow past a pipeline near a rigid bed and (2) scour around a pipeline over a sand-bed, showing favorable results for the flow and scour patterns around the pipe. The driving mechanisms of the onset and tunnel erosion are investigated by examining the detailed fluid–sediment interactions around the pipe in both regimes. The driving mechanisms for the onset and tunnel erosion are found similar in both regimes, except their time and magnitude scales. The onset is triggered by the piping mechanism induced by the upstream–downstream pressure gradient beneath the pipe. Meanwhile, the jet flow is the driving mechanism for the tunnel erosion. The simulated live-bed condition shows a higher upstream–downstream pressure gradient beneath the pipe, faster piping mechanism, more intense jet flow velocity and sediment flux compared to the clear-water condition. The model well capture these underlying mechanisms, suggesting its promising capability as a predictive tool for scouring.

CFD modeling for slurry flow through a horizontal pipe bend at different Prandtl number

The present work shows the slurry flow characteristics of bottom ash particulates having density 2219 kg/m3 at different Prandtl number through horizontal pipe bend. The simulation is carried out by adopting Eulerian two-phase model in conjunction with RNG k-ε turbulence model using available commercial software ANSYS Fluent. The transportation of solid particulates has the settling behaviour in the slurry pipeline and that leads to the sedimentation and blockage of the pipeline resulting more power and pressure drop in the pipeline. Therefore, it is important to know the transport capability of the solid particulates at different Prandtl fluids to minimise the pressure loss. The fluid properties at four Prandtl numbers i.e., 1.34, 2.14, 3.42 and 5.83 are used to carry the bottom ash concentration ranging from 40 to 60% (by weight) at mean flow-velocity ranging from 1 to 5 ms−1. The obtained computational results for pressure drop are validated with the published data in the literature and found in good agreement. The findings show that the pressure drop rises with escalation in flow velocity and Prandtl number for chosen efflux concentration range. The bottom ash particulates flowing at higher Prandtl fluid experiences less pressure drop through bend cross section in comparison to bottom ash particulates flowing at low Prandtl fluid. Finally, the contours of granular pressure, granular temperature and wall shear stress are predicted and discussed in details through the bend cross section to understand the complex slurry flow for chosen Prandtl numbers.

Numerical Simulation Study on the Layered Phenomenon of Lakes and Reservoirs Destroyed by a Forced Circulation Device

Thermal stratification is a common phenomenon in lakes and reservoirs. It has a significant influence on water quality dynamics. The destruction of the thermal stratification of lakes and reservoirs can affect the water environment, improve the water quality and the water environment quality and prevent the occurrence of eutrophication. In this study, computational fluid dynamics (CFD) combined with a Eulerian two-phase flow model is used to predict the damage caused by an airlift device to the thermal stratification phenomenon of lake water. The results show that the two devices with different sizes can contribute to a certain exchange of kinetic and thermal energy, affecting the liquid velocity and temperature in the lake water under the condition of different gas velocities. Furthermore, the degree of damage to the thermal stratification phenomenon of lake reservoir is small. However, with the same gas velocity, the device with a guide plate can have a greater impact on the liquid velocity and temperature in the lake water. Further prediction results show that the airlift installed with a guide plate can affect the heat transfer of liquid in the lake and reservoir better and destroy the thermal stratification phenomenon effectively. The quantitative results of model prediction can provide an effective basis for future field scale-up experiments.

Experimental and numerical investigations of solitary wave-induced non-equilibrium scour around structure of square cross-section on sandy berm

A series of laboratory experiments and high-fidelity numerical simulations were carried out to investigate the scour induced by a solitary wave around a non-slender, vertical structure of a square cross-section on a sandy berm. Various wave and water level combinations, structure layouts, and dimensions were studied. The flow separation at the sharp edges resulted in counterclockwise rotating out-of-plane vortices that extended from the free surface to the sandy berm. These energetic vortices were found to be the primary driving mechanism of the scouring through entraining, and entrapping the sand particles into their cores, keeping them in suspension, carrying them, and releasing them as the vortices propagate along a spiral trajectory. The analyses also showed that the flow blockage by the structure could result in flow field modulation and exacerbate the scour processes. The structure dimension appeared to be the most influential factor in the scouring process, drastically altering the characteristics of the non-equilibrium scour holes. Irrespective of the structure dimension or layout, the scour depth was greater around the seaside edge of the structure while the scour width was larger on the leeside edge. The uncertainties associated with the maximum non-equilibrium scour depth were quantified via Monte Carlo simulations which showed that the impact of the structure dimension on the maximum scour depth was almost twice more significant than that of the layout. The three-dimensional (3D) Eulerian two-phase flow numerical model, SedWaveFoam, was shown to be able to simulate sediment transport and scour around sharp-edged square structure at a low Keulegan-Carpenter ( K C ) number. • Interactions between a solitary wave and an impermeable structure placed on an erodible berm were studied experimentally. • Energetic vortices, formed at the corners of the structure, were found to be the primary driving mechanism of the scouring. • Structure dimension was the most influential factor in the scouring process. • Monte Carlo simulation was employed to assess the sensitivity of the maximum non-equilibrium scour depth to flow conditions. • SedWaveFoam model simulated scour around sharp-edged square structure at low Keulegan-Carpenter (KC) number.

Numerical Modeling of Atmospheric Rime Ice Accretion on an Airfoil Using an Eulerian Approach

AbstractThis paper presents an approach to numerically simulate the inherently unsteady rime ice accretion problem on a two-dimensional airfoil and elucidate the associated variations under different icing conditions. The airflow field and the water impingement on the airfoil are obtained based on an Eulerian two-phase model. A dynamic mesh strategy is employed to unsteadily account for the changes in the ice profile and its impact on the air and droplet flow by continuously reconstructing the computational grid at each time-step through smoothing and layering mechanisms. All main icing modules including the airflow field, droplet trajectory, icing thickness profile, and mesh management are fully coupled within the same computational framework without resorting to any external tools. Classical icing theory is employed to model the rime ice roughness, and it is assumed that the ice accretes in a direction normal to the airfoil surface. The governing Reynolds-averaged Navier–Stokes (RANS) conservation equations along with the energy and continuity equations are solved to produce the velocity and temperature fields. A convective film heat transfer coefficient is computed based on the surface heat flux and a recovery temperature which takes into account the dissipative heat release in the boundary layer in the vicinity of the airfoil surface. With the implemented strategy and calculating the convective heat transfer coefficient, the water film thickness is also calculated along with the ice shape. The model is validated by comparing the local collection efficiency distribution and ice shape with experimental data, and the results show that the implemented approach provides acceptable predictions of ice accretion profiles and rates.