Navier-Stokes Research Articles

Three-dimensional finite element analysis of turbulent crude oil flow and solid particle deposition patterns in circular curved pipelines

This study presents a numerical investigation of turbulent crude oil flows in circular curved pipelines, with a focus on the deposition patterns of solid particles within the fluid. Simulations were conducted using the Reynolds–Averaged Navier–Stokes equations coupled with the k–ε turbulence model to examine the influence of structural characteristics, such as bend curvature angle and bend curvature radius, on flow dynamics and particle deposition. The results reveal that the complex flow patterns generated by these geometric features significantly affect pressure gradients and particle trajectories. Specifically, the study shows that turbulent flows within bends exhibit intricate behaviors, with deposition patterns being strongly influenced by the pipeline’s geometric parameters. Sand particles, commonly present in petroleum flows, are found to be more effectively transported in pipes with larger curvature angles, while they exhibit a higher propensity to settle at smaller curvature angles and larger bend curvature radii. Furthermore, the simulations indicate that the majority of deposited particles accumulate on the inner wall immediately downstream of the elbow entrance.

Uniform error analysis of an exponential IMEX-SAV method for the incompressible flows with large Reynolds number based on grad-div stabilization

Based on the grad-div stabilization and scalar auxiliary variable (SAV) methods, a first-order Euler implicit/explicit finite element scheme is studied for the Navier–Stokes equations with large Reynolds number. In the designing of numerical scheme, the nonlinear term is explicitly treated such that one only needs to solve a constant coefficient algebraic system at each time step. Meanwhile, the proposed scheme is unconditionally stable without any condition of the time step τ and mesh size h. In finite element discretization, we use the stable Taylor-Hood element for the approximation of the velocity and pressure. By a rigorous analysis, we derive an uniform L2 error estimate O(τ+h2) of the velocity in which the constant is independent of the viscosity coefficient. Finally, numerical experiments are given to support theoretical results and the efficiency of the proposed scheme.

Numerical Simulation of Circulation Control for a Wing Section Using Coanda Jets

Large-eddy simulations were carried out to describe the subsonic flow over a wing section, using Coanda-jet circulation control to augment lift. The section geometry consists of a modified supercritical airfoil, with a jet that is blown over a one-quarter circular cylindrical trailing-edge Coanda surface. Because the configuration does not include a slotted trailing-edge flap, the mechanical complexity and weight may be reduced. The computations correspond to an experimental investigation, which provides data for comparison. High-fidelity solutions were obtained to the unsteady three-dimensional Navier–Stokes equations at a chord-based Reynolds number of 4.75×105 and freestream Mach number of 0.1. Several angles of attack were considered, and solutions were obtained both with and without circulation control. In the control cases, three different jet-mass flow rates were simulated at each angle of attack. A grid-resolution study was carried out to assure numerical accuracy. Comparisons are made between the respective cases and with the experimental data, and features of the flowfields are characterized. It was found that Coanda-jet control was able to augment lift in excess of factors of three with reasonable amounts of jet-mass flow.

Effects of two-dimensional reed oscillation on airflow and sound generation in a single-reed instrument

While two-dimensional (2D) reed oscillation modes of single-reed woodwind instruments have been reported in previous studies, little is known about their effects on airflow and sound generation. In this study, we conducted aeroacoustic simulations of a clarinet mouthpiece and resonator coupled with one-dimensional (1D) and 2D reed deformation models and investigated the changes in flow and sound generation due to the 2D reed vibration. The 1D and 2D reeds were modeled using 1D beam and thin plate theories, respectively, whereas the three-dimensional airflow was simulated by solving the compressible Navier–Stokes equations. The self-sustained oscillations of the 2D reed model mainly exhibited a flexural mode at the fundamental frequency, which is consistent with previous observations. Complex torsional modes were observed only at higher harmonic frequencies. A comparison between the 1D and 2D reed models demonstrated that the 2D reed opened later at the side face of the mouthpiece than the 1D reed owing to the torsional mode, which changed the time variation of the flow rate into the mouthpiece and the far-field sound in the high-frequency range. These results suggest the importance of the torsional deformation characteristics of reeds on the timbre of single-reed instruments.

Numerical study of vehicle motion during water exit under combined lifting force and wave action

During the retrieval process of the deep-sea mining vehicle (DSMV), the stability of the retrieval system is strongly influenced by the interaction between the vehicle body and the surrounding seawater due to the vehicle's complex shape and wave motion. Naturally, the negative side effects of significant changes in the vehicle's attitude and the water exit position can only increase retrieval's challenge. To investigate the characteristic of the flow field of the DSMV, this study employs the computational fluid dynamics method based on the Reynolds-averaged Navier–Stokes equations integrating the volume-of-fluid multiphase flow model with a fifth-order Stokes-wave model to explore the attitude and displacement changes of the vehicle during the water exit process in the ocean wave environment. The results indicate that the wave phase and lifting force are the major effect factors in the DSMV's water exit process. An appropriate lifting force under a specific wave phase can effectively reduce attitude changes and positional drift of the DSMV during water exit, thereby enhancing recovery efficiency and stability.

Investigating the Influence of Die Structure on the Transverse Uniformity of Slot Coating

Abstract Transverse uniformity is an important measurement of the coating quality for slot coating. In this paper, the influence of die structure on the transverse uniformity is investigated according to a fully 3D mathematical modelling and numerical simulations. In the modelling part, the coating liquid is regarded as generalized Newtonian fluid and the fluid flow inner the die head is governed by the 3D incompressible Navier-Stokes equations. In solving the model, an efficient fractional step finite element method is used. Four kinds of commonly used die structures are simulated and analysed. The results show that the die structure has great influence on the transverse uniformity. Generally, dies with double cavities can get better transverse uniformity that single cavity.

Global strong solutions to the radially symmetric compressible MHD equations in 2D solid balls with arbitrary large initial data

In this paper, we prove the global existence of strong solutions to the two-dimensional compressible MHD equations with density dependent viscosity coefficients (known as Kazhikhov-Vaigant model) on 2D solid balls with arbitrary large initial smooth data where shear viscosity μ being constant and the bulk viscosity λ be a polynomial of density up to power β. The global existence of the radially symmetric strong solutions was established under Dirichlet boundary conditions for β > 1. Moreover, as long as β>max{1,γ+24}, the density is shown to be uniformly bounded with respect to time. This generalizes the previous result [Fan et al., Arch. Ration. Mech. Anal. 245, 239–278 (2022)] of the compressible Navier-Stokes equations on 2D bounded domains where they require β > 4/3 and also improves the result [Chen et al., SIAM J. Math. Anal. 54(3), 3817–3847 (2022)] of of compressible MHD equations on 2D solid balls.

Numerical study on transonic shock wave buffeting of airfoil

Abstract Modern transportation aircraft typically cruise at transonic speeds. However, under a specific combination of incoming flow Mach numbers and angles of attack, periodic self-excited oscillations of shock waves can lead to unsteady aerodynamic loads, causing sustained vibrations in the aircraft, which is known as transonic shock wave buffeting. Buffeting loads significantly impact the fatigue life of the aircraft’s structural materials and its handling performance. In severe cases, it causes structural damage or even leads to flight safety incidents, so we should pay more attention to transonic shock wave buffeting when focusing on aeronautical engineering. This paper employs computational fluid dynamics technology for calculations to solve the Navier-Stokes equations, using the SST k-ω turbulence model to numerically simulate the steady flow field, and further employing the detached eddy simulation (DES) method to study and analyze the buffeting initiation mechanism and flow field characteristics of the NACA0012 airfoil’s transonic unsteady flow. By applying the DES method, the results demonstrate an accurate prediction of the buffeting onset boundary of the airfoil compared to wind tunnel experimental data. The research findings on the initiation mechanism and load characteristics of transonic buffeting provide a theoretical basis for optimizing the aerodynamic performance of aircraft during transonic flight and offer guidance for engineering issues such as buffeting load mitigation.

Flow field reconstruction of compressor blade cascade based on deep learning methods

In the design process of compressors, calculating the S1 flow surface involves solving the Navier-Stokes equations, which results in slow convergence and makes determining cascade characteristics time-consuming. However, deep learning offers significant advantages in flow field reconstruction by not only automatically extracting complex flow features and reducing prediction time but also providing high accuracy in reconstruction. This paper implements the rapid reconstruction of the compressor S1 flow surface cascade flow field using two deep learning models: U-Net and 1D-CNN. Using a double-circular arc airfoil as an example, we selected four key design parameters that define the geometry and position of the airfoil, ultimately designing 5,292 sets of cascade geometries. By performing batch meshing and CFD simulations, we built a cascade flow field dataset. The U-Net neural network uses design parameters as input and outputs the aerodynamic distribution of the cascade flow field. After training, it can directly predict the flow field based on the design parameters. Since the U-Net model cannot directly obtain the aerodynamic parameter distribution and flow field aerodynamic coefficients on the airfoil surface, a 1D-CNN model is used as a complementary approach. The 1D-CNN model takes the design parameters as input and outputs the aerodynamic parameter distribution on the airfoil surface and the flow field aerodynamic coefficients. The prediction results show that the U-Net model achieves an average relative error of less than 1% in cascade flow field reconstruction, while the 1D-CNN model achieves an average relative error of less than 1% in predicting the pressure recovery coefficient and less than 2% in predicting the total pressure loss coefficient. This study presents a method for the rapid reconstruction of compressor blade cascade flow fields, which helps improve design efficiency and shorten the design cycle.

Polytopic autoencoders with smooth clustering for reduced-order modeling of flows

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.

Modelling of wall-bounded cavitating flow and spray mixing in multi-component environments using the PC-SAFT equation of state

This work introduces a numerical multiphase model for multi-component mixtures, utilizing tabulated data for physical and transport properties across a spectrum of conditions from near-vacuum pressures to supercritical states. The property data are derived using Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT), vapor-liquid equilibrium (VLE) calculations, entropy scaling methodologies, and Group Contribution (GC) methods. These techniques accurately reflect the thermodynamic behaviors of real fluids, avoiding the empirical estimation of Equation of State (EoS) input parameters. Implemented in OpenFOAM, the fluid dynamics solver is designed to address the three-dimensional Navier-Stokes equations for multi-component mixtures. The methodology integrates operator splitting to manage hyperbolic and parabolic steps distinctively. Hyperbolic terms are solved using the HLLC (Harten-Lax-van Leer-Contact) solver with temporal integration performed via a third-order Strong-Stability-Preserving Runge–Kutta (SSP-RK3) method. Viscous stress tensor contributions in the momentum equation are handled through an implicit velocity correction equation, while parabolic terms in the energy equation are explicitly solved. The simulation efficiency is further enhanced by adaptive Local Time Stepping and the Immersed Boundary (IB) method, which addresses interactions between the fluid and solid boundaries. Turbulence is resolved using the Wall Adaptive Large Eddy (WALE) model. Applied to high-pressure diesel fuel spray injections into non-reacting (nitrogen) gas environments, the model has been validated against Engine Combustion Network (ECN) data for the Spray-C configuration, featuring a fully cavitating multi-hole orifice. Results demonstrate that the model achieves accurate predictions across a broad range of tested conditions without the need for tuning or calibration parameters.

Impacting factors and operation thresholds of electron transpiration cooling-based thermal protection system

Electron transpiration cooling (ETC) is a spontaneous endothermic process that occurs during thermionic emission, which shows great potential in ultra-high-temperature thermal protection systems (TPS). Herein, we systematically analyze the main influencing factors on the cooling effect of ETC, such as incoming flow velocity, geometry, and material work function. A two-dimensional finite element model, based on Navier-Stokes equations coupled with the 11-species air reaction model and two-temperature model, is developed to solve the thermal interaction between ETC and the non-equilibrium flow field. Three operational thresholds for ETC are identified. Lower work functions enhance electron emission, thereby reducing wall temperature. With a 2.0 eV work function, ETC significantly outperforms blackbody radiation at 1360 K, and its cooling efficiency increases with temperature. For flow velocities above Mach 9.0, ETC is effective at the leading edge with a 2.4 eV work function and a 5 mm radius. However, it loses effectiveness with a 300 mm leading edge radius, even at Mach 16.0. Notably, at Mach 19.6, with a 2.0 eV work function and a 5 mm radius, ETC reduces surface temperature by up to 48.1 %. These findings highlight the considerable potential of ETC for applications in ultra-high-temperature TPS. These findings highlight the considerable potential of ETC for applications in ultra-high-temperature TPS.

Simplified inverse distance weighting-immersed boundary method for simulation of fluid-structure interaction

When simulating fluid-structure interaction (FSI) problems involving moving objects, the implicit inverse distance weighting-immersed boundary method (IDW-IBM) developed by Du et al. [1] has to construct a large square correlation matrix and solve its inversion at each time step. In this work, a simplified inverse distance weighting-immersed boundary method (SIDW-IBM) is proposed to eliminate the intrinsic limitations in the original implicit IDW-IBM. Through error analysis using Taylor series expansion, a second order approximation can be derived, which allows us to approximate the large square correlation matrix into a diagonal matrix; thereby, we proposed the SIDW-IBM based on this second order approximation to explicitly evaluate the velocity corrections, where the needs to assemble the large correlation matrix and inverse it are circumvented. Owing to the fact that the inverse distance weighting interpolation removes the limitations in the Dirac delta function, the proposed SIDW-IBM has been successfully implemented on the non-uniform meshes to further improve the computational efficiency. The proposed SIDW-IBM is integrated with the reconstructed lattice Boltzmann flux solver (RLBFS) [2] to simulate some classic incompressible viscous flows, including flow past an in-line oscillating cylinder, flow past a heaving airfoil, and flow past a three-dimensional flexible plate. The good agreement between the present results and reference data demonstrates the capability and feasibility of the SIDW-IBM for simulating FSI problems with moving boundaries and large deformations.

Sintering activation energy and low-temperature sinterable process of Boron-lanthanide glass/Li2Zn3Ti4O12 ceramic composite systems for LTCC technology

This work investigates the characteristics of wettability, activation energy for sintering, evolution of phase structure, and behavior during the low-temperature sintering process of B2O3-La2O3-MgO-TiO2 (BLMT) glass/Li2Zn3Ti4O12 ceramic composites for low temperature co-fried ceramics technology (LTCC). As the BLMT glass content increases from 0 to 10 wt%, the average sintering activation energy (Ea) of the composite decreases from 450 ± 8 to 356 ± 37 kJ/mol. There are two phases the primary Li2Zn3Ti4O12 phase and the secondary LaBO3 phase, the latter precipitates from the BLMT glass after sintering at 700 °C. This indicates that BLMT glass promotes the sintering of Li2Zn3Ti4O12 ceramic below 900 °C. In composites containing 20 wt% or more glass, sintering is governed by both liquid-phase sintering and reactive viscous sintering. As the BLMT glass content increases, the impact of viscous flow on the densification process becomes more pronounced. Simultaneously, when the glass content is greater than 20 wt%, the glass precipitates LaBO3, TiO2, and MgLaB5O10 phases between 700 and 750 °C. After 850 °C, the glass melts and reacts with Li2Zn3Ti4O12 phase to produce a new TiO2 phase. Accordingly, the activation energy (Ea) of sintering the composite material increases from 393 ± 17 to 667 ± 1 kJ/mol.

Study on hydrodynamics of fish school based on SPH simulation

Abstract In this paper, the effect of spatial configurations on the hydrodynamic characteristics of fish is investigated numerically using the δ+-SPH model. The spatial configurations include side-by-side and triangular. The fluid field, including the pressure field and velocity field, are obtained by SPH simulation. The results show that the SPH method can well simulate the self-propelled movement of fish. Under the viscous flow waters, the side-by-side fish will be close to each other due to the Bernoulli effect. For triangular configurations, fish will tend to form inverted triangular configurations due to passage effects, which accompany the changes in the cost of transportation.

Rigidity‐Driven Structural Isomers in the NaCl–Ga2S3 System: Implications for Energy Storage

Alternative energy sources require the search for innovative materials with promising functionalities. Systems with unusual chemical properties represent an insufficiently explored domain, concealing unexpected features. Using diffraction and Raman spectroscopy over a wide temperature range, supported by first‐principles simulations, a rare phenomenon is unveiled: phase‐dependent chemical interactions between binary components in the NaCl–Ga2S3 system. In this unique occurrence, previously intact binary crystalline species transform upon melting into mixed liquid structural isomers, forming bonds with new partners. The chemical combinatorics appears to be fully reversible for stable crystals and liquids. Despite this, rapidly frozen glasses out of thermodynamic equilibrium remain in a metastable isomeric state, offering remarkable properties, particularly a high room‐temperature Na+ conductivity, comparable to the best sodium halide superionic conductors and therefore encouraging for sodium solid‐state batteries and energy applications. A rigidity paradigm is responsible for the observed phenomenon, as the extremely constrained Ga2S3 crystal lattice does not survive viscous flow, breaking up at a short‐range level. The removal of rigidity constraints and dense packing leads to a significant increase in empty space, which is the origin of high sodium diffusivity. Broadly, the rigidity‐driven structural isomerism opens up an inspiring path to the discovery of atypical materials.

Densification and properties of WC-CoCrFeNi/Co cemented carbide fabricated via spark plasma sintering

The spark plasma sintering (SPS) technique was used to employe WC-CoCrFeNi/Co cemented carbides, incorporating CoCrFeNi and Co as low-coercivity binder phases, resulting in the development of cemented carbides with exceptional mechanical properties. The densification mechanism varying with increasing sintering temperature and the effect of densification on the mechanical properties were investigated using the creep deformation model. In the temperature range of 1100 °C–1300 °C, the main factors contributing to densification behavior are particle rearrangement and grain boundary diffusion due to the viscous flow of the binder phase. The densification mechanism gradually transforms into dislocation climbing with increasing temperature. When the sintering temperature exceeded 1300 °C, the WC grain size increased significantly with increasing temperature and holding time, and the dominant mechanism for grain growth was grain boundary diffusion. The high densification resulted in a substantial increase in effective grain boundary area, thereby increasing both hardness and fracture toughness of the material. Benefiting from the fine grain strengthening effect of the high-entropy alloys (HEAs) and the excellent wettability of Co, a highly dense cemented carbide material with excellent hardness and fracture toughness is achieved at the sintering temperature of 1300 °C, characterized by a relative density of 99.3 %, a hardness of 2064.9 MPa, and a fracture toughness of 11.5 MPa m−2.

Retraction: “A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers” [AIP Adv. 8(2), 025315 (2018); 13(4), 025015 (2022)

Retraction: “A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers” [AIP Adv. 8(2), 025315 (2018); 13(4), 025015 (2022)

Physicochemical investigations on molecular interactions of adenine with aqueous D-glucose/D-maltose solvent media at varying temperatures and compositions

Adenine derivatives are used in pharmaceuticals, and carbohydrates like D-maltose and D-glucose which are often used as excipients or stabilizers in drug formulations. Studying their interactions can help in optimizing drug formulations for stability and effectiveness. Further, understanding their interactions, provide insights into flavor development, food stability, and potential applications in food technology. In this regard, we have analysed the physicochemical properties of adenine in aqueous saccharide solvent media which can contribute to various fields, including biochemistry, pharmaceuticals, catalysis, and material science, with use for both basic research and practical applications. So, in this research work, physicochemical properties of adenine have been investigated in aqueous and mixed aqueous (0.05, 0.10 and 0.15) mol kg−1 D-glucose/D-maltose solvent media at discrete temperatures (293.15–313.15) K and experimental pressure (0.1 MPa). The experimentally determined physical properties such as density, velocity of sound, and viscosity have been utilized for the estimation of several parameters such as apparent molar volume (Vϕ), limiting apparent molar volume (V0ϕ), hydration number (nH), limiting apparent molar expansivity (E0ϕ), Hepler’s constant (∂E0ϕ/∂T)P, apparent molar isentropic compression (Kϕ,s), limiting apparent molar isentropic compression (K0ϕ,s), viscosity B-coefficients, transfer parameters and thermodynamic parameters of viscous flow (Δμ01, Δμ02, TΔS02 and ΔH02). Further, the Co-sphere overlap model has been employed for the analysis of varied probable interactions operating in the prepared systems. The obtained results signify that in all solution systems, the solute–solvent interactions are advancing with rising temperature and concentrations of saccharides. Also, the structure breaking tendency of adenine has been investigated via inference of Hepler’s constant data and positive values of dB/dT data for all the investigated systems. Moreover, the deduced apparent specific volume data evidently specify that adenine has sweet taste in water and different concentrations of chosen saccharides.

Three dimensional branching pipe flows for optimal scalar transport between walls

Abstract We are interested in the design of forcing in the Navier–Stokes equation such that the resultant flow maximises the transport of a passive temperature between two differentially heated walls for a given power supply budget. This problem in the community is also known as ‘wall-to-wall optimal transport’ and can be reduced to optimizing the choice of the divergence-free velocity field in the advection-diffusion equation subject to an enstrophy constraint (which can be understood as a constraint on the power required to generate the flow). Previous work established that the transport cannot scale faster than 1/3-power of the power supply. Recently, Tobasco and Doering (2017 Phys. Rev. Lett. 118 264502) and Doering and Tobasco (2019 Commun. Pure Appl. Math. 72 2385–448) constructed self-similar two-dimensional steady branching flows saturating this bound up to a logarithmic correction. This correction appears to arise due to a topological obstruction inherent to two-dimensional steady flows. In this paper, we present a novel design of three-dimensional ‘branching pipe flows’ that bypasses this obstruction and, consequently, eliminates this logarithmic correction and therefore identifies the optimal scaling as a clean 1/3-power law. Our flows resemble the ones obtained in previous numerical studies of the three-dimensional wall-to-wall problem by Motoki, Kawahara and Shimizu (2018 J. Fluid Mech. 851 R4). We also discuss the implications of this result to the heat transfer problem in Rayleigh–Bénard convection and the problem of anomalous dissipation in a passive scalar.