Drag Coefficient Research Articles

Effects of Surface Turbulence Flux Parameterizations on the MJO: The Role of Ocean Surface Waves

Abstract This study investigates the sensitivity of the Madden–Julian oscillation (MJO) to changes to the bulk flux parameterization and the role of ocean surface waves in air–sea coupling using a fully coupled ocean–atmosphere–wave model. The atmospheric and ocean model components of the Energy Exascale Earth System Model (E3SM) are coupled to a spectral wave model, WAVEWATCH III (WW3). Two experiments with wind speed–dependent bulk algorithms (NCAR and COARE3.0a) and one experiment with wave-state-dependent flux (COR3.0a-WAV) were conducted. We modify COARE3.0a to include surface roughness calculated within WW3 and also account for the buffering effect of waves on the relative difference between air-side and ocean-side momentum flux. Differences in surface fluxes, primarily caused by discrepancies in drag coefficients, result in significant differences in MJO’s properties. While COARE3.0a has better convection–circulation coupling than NCAR, it exhibits anomalous MJO convection east of the date line. The wave-state-dependent flux (COR3.0-WAV) improves the MJO representation over the default COARE3.0 algorithm. Strong easterlies over the Pacific Ocean in COARE3.0a enhance the latent heat flux (LHFLX). This is responsible for the anomalous MJO propagation after the date line. In COR3.0a-WAV, waves reduce the anomalous easterlies, leading to a decrease in LHFLX and MJO dissipation after the date line. These findings highlight the role of surface fluxes in MJO simulation fidelity. Most importantly, we show that the proper treatment of wave-induced effects in bulk flux parameterization improves the simulation of coupled climate variability.

Improvement of Aerodynamic Performance of NACA 2412 Airfoil using Active and Passive Control Techniques

Improvement of Aerodynamic Performance of NACA 2412 Airfoil using Active and Passive Control Techniques

AI-based predictive approach via FFB propagation in a driven-cavity of Ostwald de-Waele fluid using CFD-ANN and Levenberg–Marquardt

The integration of Artificial Intelligence (AI) and Machine Learning (ML) techniques into computational science has ushered in a new era of innovation and efficiency in various fields, with particular significance in computational fluid dynamics (CFD). Several methods based on AI and Machine Learning (ML) have been standardized in many fields of computational science, including computational fluid dynamics (CFD). This study aims to couple CFD with artificial neural networks (ANNs) to predict the fluid forces that arise when a flowing fluid interacts with obstacles installed in the flow domain. The momentum equation elucidating the flow has been simulated by adopting the finite element method (FEM) for a range of rheological and kinematic conditions. Hydrodynamic forces, including pressure drop between the back and front of the obstacle, surface drag, and lift variations, are measured on the outer surface of the cylinder via CFD simulations. This data has subsequently been fed into a Feed-Forward Back (FFB) propagation neural network for the prediction of such forces with completely unknown data. For all cases, higher predictivity is achieved for the drag coefficient (CD) and lift coefficient (CL) since the mean square error (MSE) is within ± 2% and the coefficient of determination (R) is approximately 99% for all the cases. The influence of pertinent parameters like the power law index (n) and Reynolds number (Re) on velocity, pressure, and drag and lift coefficients is also presented for limited cases. Moreover, a significant reduction in computing time has been noticed while applying hybrid CFD-ANN approach as compared with CFD simulations only.

Multivariate state and parameter estimation with data assimilation applied to sea-ice models using a Maxwell elasto-brittle rheology

Abstract. In this study, we investigate the fully multivariate state and parameter estimation through idealised simulations of a dynamics-only model that uses the novel Maxwell elasto-brittle (MEB) sea-ice rheology and in which we estimate not only the sea-ice concentration, thickness and velocity, but also its level of damage, internal stress and cohesion. Specifically, we estimate the air drag coefficient and the so-called damage parameter of the MEB model. Mimicking the realistic observation network with different combinations of observations, we demonstrate that various issues can potentially arise in a complex sea-ice model, especially in instances for which the external forcing dominates the model forecast error growth. Even though further investigation will be needed using an operational (a coupled dynamics–thermodynamics) sea-ice model, we show that, with the current observation network, it is possible to improve both the observed and the unobserved model state forecast and parameter accuracy.

Research on Energy Loss of Optimization of Inducer–Impeller Axial Fit Dimensions Based on Wave-Piercing Theory

With the development of modern fluid machinery, the energy density of pumps is gradually being improved, and at the same time, higher demands are being placed on the cavitation performance, hence the introduction of the inducer and centrifugal impeller to form a dynamic–dynamic series structure. However, there are strict constraints on the axial size of pumps in fields such as firefighting and aerospace. The traditional empirical formula no longer satisfies the need to fit the axial dimensions between the induced wheel and the impeller at high velocities. Therefore, based on the wave-piercing theory, the drag reduction coefficient is introduced to explore the optimal axial fit size from the perspective of energy characteristics. This paper focuses on the influence of the inducer’s wake on the energy characteristics of downstream impellers, and conducts the following research: by adjusting the axial matching dimensions between the upstream inducer and the centrifugal impeller in the initial model, ten sets of axial distance models with matching dimensions of KD are designed, and the drag reduction coefficient is embedded to determine the optimal axial distance. The results show that the optimal axial distance is 0.2D, which is far lower than the axial distance value of 0.42D obtained from the traditional empirical formula for axial matching dimensions. Meanwhile, this paper uses tangential velocity, the inlet flow angle of the impeller, entropy production theory, and other indicators to analyze the internal energy loss of the high-speed vehicular fire pumps one by one. All of them confirm that the impeller in the high-speed vehicular fire pump has the lowest energy loss and optimal performance at an axial distance of 0.2D. Specifically, at this axial distance, the head can reach 259 m, and the hydraulic efficiency is as high as 83.62%. Thus, the feasibility of determining the axial placement of the impeller using the drag coefficient is validated. This research provides new insights into determining the axial coordination dimensions between the inducer and the impeller.

Aerodynamic interactions of blunt bodies free-flying in hypersonic flow

This paper takes a new look at how the aerodynamic interactions of multiple bodies in high-speed flow affect their motion behaviors. The influence of the body shape and orientation on aerodynamic and stability behavior in the case of shock–shock and wake–shock interactions is the focus of this publication. Experiments were performed in the hypersonic wind tunnel H2K at the German Aerospace Center (DLR) in Cologne. Free-flight tests with tandem arrangements of spheres and cubes were performed with a synchronized dropping of both objects at various initial conditions of relative streamwise and vertical distance as well as pitch angle. A high-speed stereo-tracking captured the model motions during free-flight, and high-speed schlieren videography provided documentation of the flow topology. Based on the measured 6-degrees-of-freedom (6DoF) motion data, aerodynamic coefficients were determined. As a result, the final lateral velocity of trailing cubes is found to be many times greater than that of spheres regarding shock-wave surfing. For rotating cubes, the results showed that stable shock-wave surfing can become possible over an increasingly wide range of initial positions. This study has identified that the trailing drag coefficient of two axially aligned objects varies strongly with their relative streamwise distance. Furthermore, it was shown that the wake is a region of stability for downstream objects.Graphical abstract

Experimental and model research on judging liquid accumulation in pipelines under the action of surfactant

Foam drainage gas extraction is applied in various natural gas extraction scenarios, such as water-bearing gas wells, gas fields with high water content, and wet natural gas pipeline transport, with the goal of enhancing extraction efficiency and lowering production costs. A common issue in foam-carrying liquid gas wells and wet natural gas pipelines is the large errors observed in the prediction model for liquid accumulation onset, derived using ellipsoidal droplets. Additionally, this model is only applicable to a single surfactant type and concentration. To investigate the effects of different types and concentrations of surfactants on the onset of liquid accumulation. This paper re-establishes the critical foam-carrying flow rate model for spherical cap-shaped foam droplets using Newton's laws of motion, through an analysis of their motion state within the air core. Through the critical foam-carrying flow rate test experiments and foam droplet deformation test experiments to obtain critical foam-carrying flow rate model in the surface tension, foam density, Weber number, drag coefficient and other parameters of the change rule and calculation method. The model's validity was further confirmed using field-measured production data from foam-carrying liquid gas wells, demonstrating accurate validation results. Compared to the previous model, this new model treats foam droplets as spherical cap-shape and introduces a dimensionless scaling factor and foaming capacity to quantify the impact of surfactant types and concentrations on foam droplet surface tension and density. This enhances the model's applicability across different types and concentrations of surfactants with greater accuracy. This offers an efficient, precise, and versatile method for predicting liquid accumulation in foam-carrying liquid gas fields, thereby enhancing the efficiency and safety of gas extraction.

A wind tunnel study of the effects of vegetation structural characteristics on the airflow field

Implementing vegetation is the preferred measure for controlling soil wind erosion. The physical variations in the wind velocity profile, such as the friction wind velocity (u*), aerodynamic roughness (z0), zero-plane displacement (d) and drag coefficient (Cd), are key to understanding soil wind erosion on vegetation-covered surfaces. However, the lack of systematic and in-depth research in the literature has led to significant controversy and uncertainty. Based on the wind tunnel data of wind velocities at 18 different heights near the ground surface for four plant heights (H = 5, 10, 15, and 20 cm) and densities (ds = 27, 46, 97, and 193 N/m2) and six free stream velocity (u∞ = 6, 8, 10, 12, 14, and 16 m/s) scenarios, the relationships among u*, z0, d, the parameters of u∞ and the vegetation structural characteristics, including the plant height (H), density (ds), and lateral cover (λ), are investigated in this paper. The conclusions are as follows: (1) The near-surface wind velocity profiles of the vegetation-covered surface can be divided into three segments with little variation in the wind velocity with height, a rapid increase in the wind velocity with height, and close to the free stream velocity. Their corresponding heights ranged from the surface to heights of 0.5 – 0.75H, 0.5 – 0.75H to 50 cm, and exceeding the height of 50 cm, respectively. (2) The zero-plane displacement increased with the plant height and density but decreased with the free stream velocity. The relationship between them can be expressed by Eq. (5). (3) The friction wind velocity of the vegetation-covered surface increased with the plant height, density, and free stream velocity. The relationship between them can be expressed by Eq. (6). The drag coefficient increased rapidly at first and then slowly decreased with increasing lateral cover, which satisfied the equation Cd = 0.00155 + 0.0111λ/(λ + 0.124). (4) The aerodynamic roughness increased with the plant height and density but decreased with the free stream velocity. The aerodynamic roughness of the vegetation-covered surface under different free stream velocities and lateral cover conditions can be expressed by Eq. (8). The study results are a basis for the modeling of the dynamics of wind erosion on vegetation-covered surfaces.

Data-driven modeling of the aerodynamic deformation and drag for a freely moving drop in the sub-critical Weber number regime

Accurate prediction of the dynamics and deformation of freely moving drops is crucial for numerous droplet applications. When the Weber number is finite but below a critical value, the drop deviates from its spherical shape and deforms as it is accelerated by the gas stream. Since aerodynamic drag on the drop depends on its shape oscillation, accurately modeling the drop shape evolution is essential for predicting the drop’s velocity and position. In this study, 2D axisymmetric interface-resolved simulations were performed to provide a comprehensive dataset for developing a data-driven model. Parametric simulations were conducted by systematically varying the drop diameter and free-stream velocity, achieving wide ranges of Weber and Reynolds numbers. The instantaneous drop shapes obtained in simulations are characterized by spherical harmonics. Temporal data of the drag and modal coefficients are collected from the simulation data to train a Nonlinear Auto-Regressive models with eXogenous inputs (NARX) neural network model. The overall model consists of two multi-layer perceptron networks, which predict the modal coefficients and the drop drag, respectively. The drop shape can be reconstructed with the predicted modal coefficients. The model predictions are validated against the simulation data in the testing set, showing excellent agreement for the evolutions of both the drop shape and drag.

Hydrodynamic efficiency limit on a Marangoni surfer

A Marangoni surfer is an object embedded in a gas–liquid interface, propelled by gradients in surface tension. We derive an analytical theorem for the lower bound on the viscous dissipation by a Marangoni surfer in the limit of small Reynolds and capillary numbers. The minimum dissipation can be expressed with the reciprocal difference between drag coefficients of two passive bodies of the same shape as the Marangoni surfer, one in a force-free interface and the other in an interface with surface incompressibility. The distribution of surface tension that gives the optimal propulsion is given by the surface tension of the solution for the incompressible surface and the flow is a superposition of both solutions. For a surfer taking the form of a thin circular disk, the minimum dissipation is $16\mu a V^2$ , giving a Lighthill efficiency of $1/3$ . This places the Marangoni surfers among the hydrodynamically most efficient microswimmers.

A study on the influence of closure model and numerical technology on the stability of two-fluid model

The influence of closure model and numerical technology on two-fluid model’s stability is studied. A stability analysis method for two-fluid model with interfacial drag term is proposed. The stability depends on the eigenvalue spectral radius of a perturbation growth rate matrix. By analyzing eigenvalue spectral radius, the effect of interfacial drag, cell size, time step and time-smoothing is studied. The main findings are: Besides interfacial drag coefficient’s magnitude, the mathematic form of drag coefficient model also has large effect. Increase of cell size, decrease of time step and time-smoothing do not necessarily lead to stability enhancement. The effectiveness of stability enhancement technology depends on relationship between spectral radius and cell size, time step and time-smoothing coefficient.

Numerical investigation of nitrogen spontaneous condensation over airfoils in cryogenic wind tunnel

Cryogenic wind tunnels (CWT) provide the aerodynamic tests that occur at high Reynolds numbers by operating under cryogenic environment to meet the requirements of hypersonic flight simulation. However, condensation in cryogenic environment near the limited condition destroys the reliability of the test measurement results. Accordingly, research on condensation in CWT is imperative for devising effective control strategies. This study introduces a transonic non-equilibrium condensation model, tailored to evaluate the complex phenomena of nitrogen condensation over airfoils. The model was applied to assess condensation effects on the NACA 0012–64 airfoil and the RAE 2822 airfoil under various operating conditions. Furthermore, the study examined the effect of the angle of attack and airfoil shape on the condensation process. The result show that nitrogen condensation near the airfoil is observable only under operating conditions within the pre-condensation zone. Operating conditions of CWT can be tailored to prevent condensation with specific airfoil profiles. The effect of condensation on the pressure coefficient includes advancing the position of the pressure jump and increasing the pressure coefficient of the airfoil intermediate region, particularly within the 20 %–70 % chord length span on the airfoil's upper surface. This primarily affects the measurement of lift coefficients in CWT. In the operating conditions of this study, the lift coefficient exhibits a maximum deviation of 31.4 %, and the drag coefficient shows a maximum deviation of 2.4 %. The transonic spontaneous condensation model offers an approach to evaluate condensation's impact on airfoil tests within CWT. The findings introduce a methodological framework for effectively controlling condensation phenomena.

Geometrical investigation of forced convective flows over staggered arrangement of cylinders employing constructal design

The current numerical work conducted a geometrical investigation of forced convective flows over a staggered arrangement of four cylinders applying constructal design. The main objectives are to determine designs maximizing the Nusselt number (NuD) and minimizing the drag coefficient (CD) of the cylinders at three distinct Reynolds numbers (ReD = 10, 40, and 150) considering Pr = 0.71. The problem involves two constraints: cross-sectional area of the cylinders and the occupation area of the arrangement, and three degrees of freedom: ST/D, SL1/D and SL2/D. These represent the ratios between the transversal pitch, the longitudinal pitch between the frontal and intermediate cylinders, and the longitudinal pitch between the intermediate and posterior cylinders over the diameter. The introduction of two longitudinal pitches enabled an exploration of the generation of asymmetrical patterns in the flow direction. Results indicated a strong dependency of the arrangement design on the Reynolds number. Moreover, asymmetrical configurations generally benefited both performance indicators for the present conditions. The most favorable arrangements for the fluid dynamics were achieved with the lowest ST/D, more concentrated longitudinal pitches for ReD = 10, and asymmetrical pitches for ReD = 40 and 150. Concerning the thermal purpose, the highest magnitude of ST/D and asymmetrical longitudinal pitches led to the highest NuD. For ReD = 10, the intermediate cylinders are near the upstream one; for ReD = 40 the length of the arrangement increases with the intermediate cylinders near the downstream one, and for ReD = 150, the arrangement occupied all the length of occupation area with slight asymmetry.

Clap-and-Fling Mechanism of Climbing-Flight Coccinella Septempunctata.

Previous studies on the clap-fling mechanism have predominantly focused on the initial downward and forward phases of flight in miniature insects, either during hovering or forward flight. However, this study presents the first comprehensive kinematic data of Coccinella septempunctata during climbing flight. It reveals, for the first time, that a clap-and-fling mechanism occurs during the initial upward and backward phase of the hind wings' motion. This discovery addresses the previously limited understanding of the clap-and-fling mechanism by demonstrating that, during the clap motion, the leading edges of beetle's wings come into proximity to form a figure-eight shape before rotating around their trailing edge to open into a "V" shape. By employing numerical solutions to solve Navier-Stokes (N-S) equations, we simulated both single hind wings' and double hind wings' aerodynamic conditions. Our findings demonstrate that this fling mechanism not only significantly enhances the lift coefficient by approximately 9.65% but also reduces the drag coefficient by about 1.7%, indicating an extension of the applicability range of this clap-and-fling mechanism beyond minute insect flight. Consequently, these insights into insect flight mechanics deepen our understanding of their biological characteristics and inspire advancements in robotics and biomimetics.

Determination Of Drag And Inertia Coefficients By An Analytical Model

Hard structures like dykes or groins have been recognized for their negative environmental impact and limited durability in the face of climate change (Sutton-Grier et al., 2015). The concept of Shore Soft Engineering (SSE) has allowed ecological considerations to be embedded in the design of coastal protection (Hartig et al., 2011). Among emerging defense structures, nature-based solutions are built with natural materials and rely on physical properties and mechanisms observed in nature. They aim to protect, manage and restore ecosystems while providing some benefit to the human-being and biodiversity (Cohen-Shacham et al., 2016); they offer an interesting alternative to hard structures. However, implementing these solutions in urbanized coastal areas where ecosystems are vulnerable can be challenging. Another alternative approach is using biomimetic solutions, which can provide the functions of natural systems like seagrass, dunes, or coral through robust human-made constructions. Natural habitats exist in a variety of more or less complex forms, ranging from rigid (mangroves, coral) to flexible (seagrass) (Mullarney and Henderson, 2018); and they drive changes in the current profile, in wave dissipation or in sediment motion. Understanding how to mimic these systems, in particular their internal geometry and hydrodynamic effects, is challenging. This complexity makes the development of biomimetic solutions difficult (Perricone et al., 2023). In this context, this study strictly focuses on wave dissipation by flexible systems. Wave dissipation by natural habitats has been extensively studied through laboratory experiments (Houser et al., 2015) and in-situ measurements (Bradley and Houser, 2009). The pioneer analytical model (Dalrymple et al., 1984) depicted aquatic vegetation as rigid cylinders; however, the rigidity assumption fails to capture the inherent flexibility of plants. Alternative strategies emerged to account for this flexibility, such as using an empirical drag coefficient (Mendez and Losada, 2004) or introducing an effective length, representing the length that a rigid cylinder would have to dissipate the same wave height as flexible cylinders (Luhar and Nepf, 2016). However, to define this effective length or an empirical drag coefficient, it is necessary to carry out in-situ measurements. Numerous analytical models based on force balance (Luhar and Nepf, 2016; Leclercq and de Langre, 2018) have been developed to represent the movement of flexible vegetation like seagrass. These models depict the flexible vegetation as a series of segmented rigid stems attached to each other and subjected to oscillating flows. Some models attempt to link stem motion with wave dissipation to integrate this coupling into numerical models (Yin et al., 2022). However, these models still require unknown quantities such as drag and inertial coefficients. The present study aims to develop an analytical model for determining drag and inertial coefficients based solely on the geometry, the structure flexibility and wave forcing. At last, the method could help better represent the dissipation into numerical simulations without the need for prior parametrization.

Sensitivity analysis and calibration of a Lagrangian particle tracking using GPS-tagged drifters

A Lagrangian particle tracking module within a hydrodynamic model in Environmental Fluid Dynamic Code Plus (EFDC+) was used to track the movements of large floating marine carcasses. This research used data from six GPS-tagged drifters collected in April 2017 by NOAA to conduct a sensitivity analysis and calibration on the Lagrangian particle tracking module. These analyses investigate the influence of specific parameters, notably wind drag and number of vertical layers in the model. Changing these parameters resulted in observable changes in the trajectories of tracked particles. The results of the sensitivity experiments were compared using the Skill Score statistic. Adding wind drag to the LPT was a pivotal alteration, augmenting the model predictive capabilities by increasing the Skill Score value from 0.23 to 0.47. Further tests examined the impact of varying wind drag coefficients (A and B) which are the slope and y-intercept of a linear equation used to describe overall drag coefficient (CD) as a function of wind velocity. These coefficients are employed in EFDC + software and altering them revealed that coefficient A has a larger impact on the model predictions compared to coefficient B. Finally, the transition from a 2D to a 3D model had a more significant impact on the results compared to increasing the number of vertical layers in the 3D configuration. However, the findings indicated that changing the model from 2D to 3D may not yield a large enough improvement in accuracy that would justify the additional computational demands associated with a 3D model when running long periods of time (several years). The study results have valuable implications for developing accurate and precise models of hydrodynamic systems emphasizing the importance of wind in LPT models and the efficiency of 2D vs 3D models for LPT simulations in the Mississippi Sound area.

Stall characteristics of wavy leading-edge airfoil in subsonic and transonic airflows

Based on the bioinspired wavy leading-edge, the stall characteristics of the NACA0012 airfoil are optimized. In this paper, the semicircle plus line segment is used to obtain the wavy leading edge. The aerodynamic forces of the airfoil are measured by a high-precision balance, and the detailed flow features of the airfoil are obtained by the oil flow tests. Then, combined with numerical simulation, the optimization mechanism is obtained. The operating conditions are as follows: Mach number ranging from 0.4 to 0.8, and angle of attack ranging from −4° to 25°. The results show that in high speed airflows, compared with the basic airfoil, the lift coefficient of the wavy leading-edge airfoil does not decrease sharply with the increase of the angle of attack, and the drag coefficient of the wavy leading-edge airfoil is similar to the basic airfoil; among the three types of airfoils studied, the larger wavy leading-edge feature size has better aerodynamic characteristics; combined with the numerical simulation results, it can be seen that the stall mechanism of airfoils varies at different Mach numbers. The wavy leading-edge generate streamwise vortex. The streamwise vortices increase energy transport in the boundary layer. Therefore, the separation zone moves toward the trailing edge of the airfoil, and the stall characteristics of the airfoil are optimized.

Sugarcane leaf return and mixing significantly reduce slope runoff and soil loss

AbstractImproper management of sugarcane cultivation may cause severe soil erosion, especially in lateritic red soil hilly areas. Crop straw return to the field can effectively improve the soil structure, but there is a lack of evaluation studies of the soil and water conservation benefits of sugarcane leaf mixing and return to the field, and the underlying regulatory mechanism has rarely been described. Thus, we conducted a series of simulated rainfall experiments to investigate the impact of returning different mixed sugarcane leaf weights (0, 3, 6, 9, 12 and 15 t/ha) to the field on erodible lateritic red soil slopes that support sugarcane production under various slopes (5°, 10°, 15° and 20°) in different rainfall events (60 and 120 mm/h). The results indicated that returning sugarcane leaves into farmland could effectively regulate the process of runoff and sediment production on lateritic red soil slopes, and the optimal mixing amount was 9 t/ha. Under a low rainfall intensity, the erosion process was mainly affected by the slope, and the benefits of applying the sugarcane leaf mixing treatment to the slope to reduce runoff and sediment could reach 13.37–53.04% and 23.86–77.55%, respectively. However, under a high rainfall intensity, the sugarcane leaf mixing amount was the main influencing factor, the benefits for reducing runoff and sediment could reach 4.64–38.72% and 30.87–93.14%, respectively. The sugarcane leaf mixing amount exhibited a linear relationship with the Reynolds number (R2 > 0.63), whereas the runoff velocity (R2 > 0.96), Froude number (R2 > 0.94) and drag coefficient (R2 > 0.85) exhibited well‐fitting exponential function relationship with it. This study provides a reference for future endeavours regarding the inhibition mechanisms of sugarcane leaves mixed and returned to the field for decreasing slope erosion.

Flow past a random array of statistically homogeneously distributed stationary Platonic polyhedrons: Data analysis, Probability maps and Deep Learning models

We perform particle-resolved direct numerical simulations (PR-DNS) of the flow past a random array of stationary Platonic polyhedrons seeded in a tri-periodic box at Reynolds number Re=1, 10, and 100 and solid volume fraction 0.05, 0.1 and 0.2. Using Platonic polyhedrons enables us to examine the effects of particle angularity on the hydrodynamic force and torque exerted on the stationary particles in a controlled manner. We report the average drag, lift, and torque coefficients as well as their respective distribution. We explore the relationship between the particle angularity, particle angular position, flow disturbances created by the neighboring particles, and the hydrodynamic force and torque exerted on each individual particle. We attempt to extend our probability map based model (MPP), our Physics Informed neural network (PINN) model previously developed for spheres to Platonic polyhedrons, and propose an additional NN architecture. We show that ignoring the angular position and actual shape of the reference and neighboring particles constitutes a reasonable first order approximation that significantly simplifies the construction of deterministic models of hydrodynamic forces and torques at low Re=1 to moderate Re=10. At high Re=100, both the MPP model and the PINN model without any additional knowledge of the particle shape and angular position fail to properly predict the force and torque fluctuations. We then design a Convolutional Neural Network (CNN) architecture that is able to maintain a satisfactory performance at Re=100 but requires additional input data in the form of a coarse-grained velocity field around each particle. Overall, predicting the torque fluctuation remains a significant challenge.

Thompson and Troian slip effect on ternary nanofluid flow over a stretching surface influenced by induced magnetic field and surface catalyzed reaction

This research scrutinizes the impact of the Thompson and Troian slip effect on a two-dimensional flow of ternary nanoliquid induced by an extending sheet near a stagnation point. Nanoparticles Iron oxide (Fe2O3), Nickle Zinc ferrite (NiZnFe2O4), and Magnesium zinc iron oxide (MnZnFe2O4) are dispersed in Ethylene glycol (C2H6O2) to establish ternary nanofluid. The induced magnetic field influences the flow, and the analysis of heat and mass transfers takes into account the Cattaneo–Christov (C–C) heat flux with homogenous–heterogeneous (H–H) reactions, respectively. To expedite the reaction, a surface-catalyzed process is introduced to efficiently control both (H–H) reactions within a reduced time frame. Utilizing the Tiwari and Das framework, the fluid flow characteristics are elucidated. Appropriate transformations are applied to derive ordinary differential equations (ODEs), which are then numerically deciphered via the bvp4c scheme. Graphs are portrayed to highlight the consequence of non-dimension quantities on the flow and temperature profiles. The surface drag coefficient and heat flux rate are also assessed and summarized. Outcomes revealed that for large estimates of the velocity slip parameter, the surface drag coefficient is enhanced while the heat flux rate is reduced. It is also interesting to note that because of the high estimations of ferromagnetic nanoparticles, the rate of heat transfer is elevated significantly. The validation of the proposed model is also included.