Direct Numerical Simulation Method Research Articles

A numerical study of Elasto-inertial particle-focusing in straight and serpentine microchannels

Microfluidic devices have gained popularity in recent years due to their low cost and simplicity. Cell focusing linked with cell counting and cell separation used in clinical tests and point-of-care devices stands towards the top of every list of microfluidic applications. To focus and manipulate particles in a Newtonian medium, inertial microfluidics has been widely used. There is a requirement to replace a significantly more efficient approach given various particle-focusing positions near the channel walls recorded by inertial microfluidics. Here, the synergetic effect of elastic and inertial forces in relatively low-concentration viscoelastic fluids was investigated numerically. Utilizing particle-focusing behavior in straight and serpentine channels with different corner angles, by applying the numerical results obtained using the developed direct numerical simulation method (DNS) for elastic and inertial forces, we created a microchannel with a remarkable performance. As the flow regime transitions to elasto-inertial, where inertial forces are comparable to elastic forces in a straight microchannel, particles tend to concentrate at the channel centerline. As the flow rate increases, however, particle defocusing develops, and shear gradient lift forces ultimately overcome elastic forces in the channel's central region. Given that fluid flows at a higher velocity in the serpentine channel with a corner angle of 75° than in other channels, the Dean drag force induced by secondary flow serves to reduce particle defocusing rate at a given flow rate, making this channel a desirable platform for Elasto-inertial microfluidics. Particle focusing in a vertical direction was noticed as a benefit of elasto-inertial microfluidics, regardless of the geometry or flow rate of the particles passing through the channel. Finally, the impact of particle diameter on focusing behavior was studied. As particle diameter decreases, focusing width decreases and the focusing band shifts to the left side of the cross-section. We expect that the numerical evaluation of using viscoelastic medium in complex geometries can contribute to accelerate the three dimensional particle-focusing mechanism and enhance the efficiency of microdevices for cell and particle manipulation.

Investigation of the flow-heat-vortex mechanism in hot, coolant and delivery channels in film cooling under strongly-coupled boundary conditions using direct numerical simulation

The research investigated the flow dynamics, heat transfer, and vortices in film cooling using direct numerical simulation (DNS) with various blowing ratios (Br = 0.63, 0.86, 1.18) and Reynolds numbers (Re = 1000, 1000, 500) at an injection angle of α = 20°. The strongly-coupled (SCP) boundary conditions were applied to solve the transient governing equations including to mass and momentum conservations, thermal convection and heat conduction. Jetting effects in the delivery channel were studied by the DNS method in the environment of both hot and coolant channels. Distinctive vortex structures, including the horseshoe and hairpin vortices inside the delivery channel, were successfully identified with the recirculation and high-velocity stripes inside the channel. The heat-transfer mechanisms resulting from the vortices in hot channel highlighted the presence of kidney-shaped and reverse-kidney-shaped vortices impacting the Nusselt number (Nu) and comprehensive cooling effectiveness, which was enabled by the state-of-the-art VI method of Liutex.

Pore-scale investigation of forced imbibition in porous rocks through interface curvature and pore topology analysis

Forced imbibition, the invasion of a wetting fluid into porous rocks, plays an important role in the effective exploitation of hydrocarbon resources and the geological sequestration of carbon dioxide. However, the interface dynamics influenced by complex topology commonly leads to non-wetting fluid trapping. Particularly, the underlying mechanisms under viscously unfavorable conditions remain unclear. This study employs a direct numerical simulation method to simulate forced imbibition through the reconstructed digital rocks of sandstone. The interface dynamics and fluid–fluid interactions are investigated through transient simulations, while the pore topology metrics are introduced to analyze the impact on steady-state residual fluid distribution obtained by a pseudo-transient scheme. The results show that the cooperative pore-filling process promoted by corner flow is dominant at low capillary numbers. This leads to unstable inlet pressure, mass flow, and interface curvature, which correspond to complicated interface dynamics and higher residual fluid saturation. During forced imbibition, the interface curvature gradually increases, with the pore-filling mechanisms involving the cooperation of main terminal meniscus movement and arc menisci filling. Complex topology with small diameter pores may result in the destabilization of interface curvature. The residual fluid saturation is negatively correlated with porosity and pore throat size, and positively correlated with tortuosity and aspect ratio. A large mean coordination number characterizing global connectivity promotes imbibition. However, high connectivity characterized by the standardized Euler number corresponding to small pores is associated with a high probability of non-wetting fluid trapping.

Optimization and Modelling to Enhance Hydroturbine Performance

In this study, a new design of a hydroturbine was developed, modelled, and constructed. The unique features of this turbine design required a thorough investigation and optimization process to enhance hydroturbine performance. The paper discusses numerical and experimental results obtained on the hydroturbine. The optimal angle of attack for the inlet flow direction has been computed from numerical modelling. Consequently, data on velocity, pressure, lift, and drag forces along the blade have been obtained. The study also takes into account the operation of the hydroturbine under non-rotating and rotating rotor modes. Performance metrics such as head, torque, hydraulic power, hydroturbine power, and efficiency were then calculated based on water discharge. These performance calculations were conducted using COMSOL Multiphysics, employing Direct Numerical Simulation and k-epsilon methods. Numerical calculations offer a cost-effective approach to reducing the financial burden associated with material costs for manufacturing hydroturbine prototypes.

A hybrid pore-network-continuum modeling framework for flow and transport in 3D digital images of porous media

Understanding flow and transport in multiscale porous media is challenging due to the presence of a wide range of pore sizes. Recent imaging advances offer high-resolution characterization of the multiscale pore structures. However, simulating flow and transport in 3D digital images requires models to represent both the resolved and sub-resolution pore structures. We develop a hybrid pore-network-continuum modeling framework. The hybrid framework treats the smaller pores below the image resolution as a continuum using the Darcy-scale formalism and explicitly represents the larger pores resolved in the images employing a pore network model. We validate the hybrid model against direct numerical simulations for single-phase flow and solute transport and further demonstrate its applicability for simulating two-component gas transport in a shale rock sample. The results indicate that the new hybrid model represents the flow and transport process in multiscale porous media while being much more computationally efficient than direct numerical simulation methods for the range of simulated conditions.

Development of Node-centered finite-volume diffusion method on triangle mesh for detonation propagation simulation in insensitive high explosives

This study presents a numerical simulation of detonation waves in insensitive high explosives (IHE). A direct numerical simulation (DNS) method of detonation waves propagation was developed. It solves two-dimensional reactive Euler equations by using a semi-discrete node-centered finite-volume (NCFV) scheme on triangle mesh. Employing ZND model analytical solution as the initial condition, the upper and lower boundary conditions were designed as local sonic equilibrium conditions. The DNS method was validated using steady detonation wave propagation experimental results for tri-amino-tri-nitro-benzene (TATB) based explosives. The two-dimensional steady detonation propagation of the circular arc experiments was completed using a non-embedded technique (electric and optical fibre probe velocimetry). The comparison results demonstrate that the numerical method can provide a good prediction of the pseudo-steady-state detonation wave front propagation and the angular speed.

A particle-resolved direct numerical simulation method for the compressible gas flow and arbitrary shape solid moving with a uniform framework

Compressible particle-resolved direct numerical simulations (PR-DNS) are widely used in explosion-driven dispersion of particles simulations, multiphase turbulence modelling, and stage separation for two-stage-to-orbit vehicles. The direct forcing immersed boundary method (IBM) is a promising method and widely applied in low speed flow while there is few research regarding compressible flows. We developed a novel IBM to resolve supersonic and hypersonic gas flows interacting with irregularly shaped multi-body particle. The main innovation is that current method can solve the interaction of particles and high-speed fluids, particle translation and rotation, and collision among complex-shaped particles within a uniform framework. Specially, high conservation and computation consumption are strictly satisfied, which is critical for resolving the high speed compressible flow feature. To avoid the non-physical flow penetration around particle surface, an special iterative algorithm is specially derived to handle the coupling force between the gas and particles. The magnitude of the velocity difference error could be reduced by 6–8 orders compared to that of a previous method. Additionally, aerodynamic force integration was achieved using the momentum equation to ensure momentum conservation for two-phase coupling. A high-efficiency cell-type identification method for each step was proposed, and mapping among LPs and cells was used again to select the immersed cells. As for the collision force calculation, the complex shape of a particle was represented by a cloud of LPs and the mapping of LPs and cells was used to reduce the complexity of the algorithm for contact searching. The repetitive use of the mapping relationship could reduce the internal memory and improve the efficiency of the proposed algorithm. Moreover, various verification cases were conducted to evaluate the simulation performance of the proposed algorithm, including two- and three-dimensional moving and motionless particles with regular and complex shapes interacting with high-speed flow. Specifically, an experiment involving a shock passing through a sphere was designed and conducted to provide high-precision data. The corresponding results of the large-scale numerical simulation agree well with those obtained experimentally. The current method supports flow simulations at a particle-resolved scale in engineering.

Dynamic analysis and performance evaluation of inerter fractional nonlinear quasi-zero stiffness isolator on a multi-span bridge under moving load

In this paper we propose a new vibration isolator system, which combines the advantages of a quasi-zero stiffness (QZS) isolator, a damper exhibiting fractional properties and an inerter, to reduce the vibrations of a multi-span continuous beam bridge excited by moving loads. The inerter produces a fictitious mass amplification effect to improve the controller performance and the fractional order takes into account the previous state of the viscoelastic material. After formulating the dynamics equation using beam theory, the amplitude response is determined analytically using the averaging method. The results obtained from the analytical study are validated using the direct numerical simulation method (Newton–Leipnik method). By comparing the isolation performance of the FQZS (fractional quasi-zero stiffness) isolator and the IFQZS (inerter fractional quasi-zero stiffness) isolator, it is shown that the addition of inertance can significantly suppress the tendency of the curve to slope to the right, allowing us to have a wider isolation frequency range on force transmissibility while improving the efficiency of the isolator. One also shows that increasing the fractional parameter contributes to a decrease in the vibration amplitude of the structure, the amplitude of the force transmitted and the area in which unstable solutions appear. However, beyond a certain value of the fractional parameter, we observe an increase in the latter. In order to further extend the study, bifurcation diagram, phase portrait, time history and power spectral density are explored.

Simulating Brownian motion in thermally fluctuating viscoelastic fluids by using the smoothed profile method

To investigate the Brownian motion of individual particles suspended in viscoelastic fluids, the stochastic smoothed profile method (SPm) for direct numerical simulation is developed by extending deterministic SPm for suspensions in viscoelastic media. To simulate viscoelastic flow driven by thermal fluctuations in the suspending medium, the random stress in the fluid momentum equation as well as the random driving force for the conformation tensor in the Oldroyd-B model are incorporated according to the fluctuating hydrodynamics and fluctuating viscoelasticity formalisms. The thermal equilibrium and dynamical properties calculated by using numerical simulations successfully reproduce the analytic predictions, validating the direct simulation for the coupled fluctuating Navier–Stokes and Oldroyd-B equations and for the coupling between the stochastic viscoelastic medium and individual particles. As an application of the stochastic SPm, we investigate finite system-size effects under periodic boundary conditions (PBCs) on the passive microrheological relationship between the mean-square displacement (MSD) of a Brownian particle and the medium's dynamic modulus. Comparing the modulus that was microrheologically calculated from the MSD with the input modulus reveals that the effect of periodic image cell interaction appears not only in the long-time diffusive regime but also in the short-time region. A frequency-dependent finite system-size correction is implemented by phenomenologically extending the long-time diffusive regime correction, allowing passive microrheology analysis under PBCs. This result can be directly applied to other mesoscale numerical simulations including coarse-grained molecular dynamics and dissipative particle dynamics simulations.

Deep learning architecture for sparse and noisy turbulent flow data

The success of deep learning models in fluid dynamics applications will depend on their ability to handle sparse and noisy data accurately. This paper concerns the development of a deep learning model for reconstructing turbulent flow images from low-resolution counterparts encompassing noise. The flow is incompressible through a symmetric, sudden expansion featuring bifurcation, instabilities, and turbulence. The deep learning model is based on convolutional neural networks, in a high-performance, lightweight architecture. The training is performed by finding correlations between high- and low-resolution two-dimensional images. The study also investigates how to remove noise from flow images after training the model with high-resolution and noisy images. In such flow images, the turbulent velocity field is represented by significant color variations. The model's peak signal-to-noise ratio is 45, one of the largest achieved for such problems. Fine-grained resolution can be achieved using sparse data at a fraction of the time required by large-eddy and direct numerical simulation methods. Considering its accuracy and lightweight architecture, the proposed model provides an alternative when repetitive experiments are complex and only a small amount of noisy data is available.

Acoustic radiation of bubble clusters with different volume fractions

Cavitation noise, mainly from bubble cluster collapse, is a primary source of noise in underwater equipment. This study aims to elucidate the acoustic characteristics of bubble clusters with varying volume fractions (0.002%–43%), thereby illuminating the noise patterns generated during bubble cluster collapse. With the direct numerical simulation (DNS) method, we simulate the collapse of bubble clusters containing 352 vapor bubbles. Far-field sound pressure was calculated by using the Farassat 1 A integral solution of the Ffowcs Williams–Hawkings (FW–H) equation. The results show that when the volume fraction of bubble clusters is greater than 20%, the higher the volume fraction, the closer the far-field sound pressure radiated by its collapse is to that of the equivalent bubble (whose volume is equal to the volume of the bubble cluster), and when the volume fraction is greater than 30%, the sound pressure of the bubble cluster is basically the same as that of the equivalent bubble. Furthermore, when the volume fraction of bubble clusters is less than 1%, the lower the volume fraction is, the closer the sound pressure obtained through the superposition of a single bubble (each with an initial radius equal to that within clusters and in a free field) is to that of bubble clusters, and when the volume fraction is less than 0.1%, the bubble clusters' sound pressures agree with those obtained through superposition. This study reveals the far-field noise pattern generated by the collapse of bubble clusters, providing a theoretical basis for the prediction of cavitation noise.

Interface coupling effect and multi-mode Faraday instabilities in a three-layer fluid system

We investigate the Faraday instabilities of a three-layer fluid system in a cylindrical container containing low-viscosity liquid metal, sodium hydroxide solution and air by establishing the Mathieu equations with considering the viscous model derived by Labrador et al. (J. Phys.: Conf. Ser., vol. 2090, 2021, 012088). The Floquet analysis, asymptotic analysis, direct numerical simulation and experimental method are adopted in the present study. We obtain the dispersion relations and critical oscillation amplitudes of zigzag and varicose modes from the analysis of the Mathieu equations, which agree well with the experimental result. Furthermore, considering the coupling strength of two interfaces, besides zigzag and varicose modes, we find a beating instability mode that contains two primary frequencies, with its average frequency equalling half of the external excitation frequency in the strongly coupled system. In the weakly coupled system, the $A$ -interface instability, $B$ -interface instability and $A$ & $B$ -interface instability are defined. Finally, we obtain a critical wavenumber $k_c$ that can determine the transition from zigzag or varicose modes to the corresponding $A$ -interface or $B$ -interface instability.

Stability Analysis for High-Speed Boundary-Layer Flow with Cavities

This study uses direct numerical simulation and stability analysis methods to investigate the impact of wall cavity defects on the instability of boundary layers at Ma=5.92 and Ma=1.38. For flow at Ma=5.92, synchronization points with equal phase velocities in both fast and slow modes play a crucial role in controlling disturbance wave growth. When the inlet disturbance wave frequency (ω=0.98) approaches the synchronization point frequency, the impact of cavity size on the growth of the disturbance wave can be divided into three regions in the (L/δ99, D/δ99) plane, namely, region A, region B, and region C. Region A refers to small cavities with L/δ99<2, which have the weakest suppression effect. Region B includes large cavities with L/δ99>2 and D/δ99<1.5 and exhibits the best suppression effect. Finally, region C covers cavities with L/δ99>3 and D/δ99>1.5 and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at Ma=1.38, cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities (L/δ99>5, D/δ99<2) exhibit the most significant enhancement.

Hydrodynamic force interaction of two fixed spheres in a wall-bounded linear shear flow

We examine the modulations of the drag coefficient Cd and lift coefficient Cl on a spherical particle caused by the presence of a neighboring sphere when positioned in close proximity to a wall. Data are generated through the utilization of a fast and accurate Particle-Resolved Direct Numerical Simulation (PR-DNS) method that relies on the Direction-Splitting algorithm and that was extensively validated in our prior study (Goyal and Wachs, 2023a, 2023b; Morente et al., 2023). We further validate the method in the flow configuration of the present study by comparing them with data published in the literature. We consider three Reynolds numbers Re=20, Re=50 and Re=100, which describe the flow conditions in the vicinity of the wall. The primary sphere is positioned at a distance δ from the wall, while the neighboring sphere is positioned at a constant distance from the primary sphere encompassing all possible angular positions θ. We report the modulations of Cd and Cl compared to a situation without any neighboring sphere as a function of δ, θ and Re. The inclusion of a wall intensifies the influence of the neighboring sphere on the primary sphere and significantly modifies the values of Cd and Cl. We attempt to relate the values of the modulations of Cd and Cl to the modulations in the contours of the pressure and of the spanwise vorticity on the surface of the primary sphere. We take advantage of the periodic nature of Cd and Cl as a function of the relative angular position θ of the neighboring sphere and propose a Fourier Predictive Model (FPM) to effectively represent the data using a finite number of modes in the cosine Fourier series. We show that our FPM is able to estimate the modulations of Cd and Cl excellently with a coefficient of determination R2≳0.99 in the parameter space investigated in our study.

A GPU-ready pseudo-spectral method for direct numerical simulations of multiphase turbulence

In this work, we detail the GPU-porting of an in-house pseudo-spectral solver tailored towards large-scale simulations of interface-resolved simulation of drop- and bubble-laden turbulent flows. The code relies on direct numerical simulation of the Navier-Stokes equations, used to describe the flow field, coupled with a phase-field method, used to describe the shape, deformation, and topological changes of the interface of the drops or bubbles. The governing equations – Navier-Stokes and Cahn-Hilliard equations – are solved using a pseudo-spectral method that relies on transforming the variables in the wavenumber space. The code targets large-scale simulations of drop- and bubble-laden turbulent flows and relies on a multilevel parallelism. The first level of parallelism relies on the message-passing interface (MPI) and is used on multi-core architectures in CPU-based infrastructures. A second level of parallelism relies on OpenACC directives and cuFFT libraries and is used to accelerate the code execution when GPU-based infrastructures are targeted. The resulting multiphase flow solver can be efficiently executed in heterogeneous computing infrastructures and exhibits a remarkable speed-up when GPUs are employed. Thanks to the modular structure of the code and the use of a directive-based strategy to offload code execution on GPUs, only minor code modifications are required when targeting different computing architectures. This improves code maintenance, version control and the implementation of additional modules or governing equations.

A data-driven framework for designing microstructure of multifunctional composites with deep-learned diffusion-based generative models

This paper introduces a novel integrated microstructure design methodology that replaces the common existing design approaches for multifunctional composites: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of materials. The problem of microstructure reconstruction is addressed using the diffusion-based generative model (DGM), which is a state-of-the-art generative model formulated with a Markovian diffusion process. Then, the conditional formulation of DGM is introduced for guidance to the embedded desired material properties with a transformer-based attention mechanism, which enables the inverse design of multifunctional composites. Furthermore, a convolutional neural network (CNN)-based surrogate model is utilized to facilitate the prediction of linear/nonlinear material properties for building microstructure-property linkages. Combined, the proposed artificial intelligence-based design framework enables large data processing and database construction that is often not affordable with resource-intensive finite element method (FEM)-based direct numerical simulation (DNS) or iterative reconstruction methods. It is worth noting that the proposed DGM-based methodology is not susceptible to unstable training or mode collapse, which are common issues in generative models that are often difficult to address even with extensive hyperparameter tuning. An example case is presented to demonstrate the effectiveness of the proposed approach, which is designing mechanoluminescence (ML) particulate composites. The results show that the designed ML microstructure samples with the proposed generative and surrogate models meet the multiple design requirements (e.g., volume fraction, elastic constant, and light sensitivity). This assessment demonstrates that the proposed integrated methodology provides an end-to-end solution for practical material design applications.

Direct Numerical Simulation Method of Turbulence Taking the History of the Process into Account

Direct Numerical Simulation Method of Turbulence Taking the History of the Process into Account

Induced-charge electroosmosis flow of viscoelastic fluids under different voltage arrangements

Efficient mixing of chemical analysis reagents with laboratory samples at a microscale is a key issue in numerous biomedical and chemical analyses but hardly to implement due to the limited of the low diffusivity in laminar flow. Induced-charge electroosmosis flow, as an innovative mixing method, has been proved to be effective and simple in rapid mixing attributes to its mechanism of vortex generation. This work aims to propose a new strategy for chaotic induced-charge electroosmosis flow based on different voltage arrangements to improve the mixing of viscoelastic fluids. The Phan–Thien–Tanner constitutive model is applied to characterize the flow behavior of viscoelastic fluid in a microfluidic preparation mixer. The direct numerical simulation method is used to solve the fully coupled Navier–Stokes and Poisson–Nernst–Planck equations for a polarizable cylinder in a two-dimensional cavity filled with electrolyte solution. The impact of Weissenberg number (Wi), Debye parameter, voltage strength on the velocity, net charge density, and potential profiles is investigated. The simulation results indicate that a greater Wi leads to the decrease in the maximum velocity, and a large voltage strength can heighten the net charge density and potential, thus improve the peak velocity. Moreover, the classical theoretical prediction that the maximum velocity is proportional to the square of the applied voltage has been authenticated.

Study of the hydraulic roughness impact on turbulent heat transfer at supercritical pressure based on a fast direct numerical simulation method

A numerical experiment on turbulent heat transfer of supercritical fluids (SCFs) in hydraulically rough heating tubes is performed using a fast direct numerical simulation method for characterizing hydraulic roughness. The objective is to assess the impact of hydraulic roughness on SCF turbulent flow and heat transfer and delve into the underlying mechanism. Four cases are simulated, including one case of smooth flow and three cases with varying roughness parameters. The simulations are conducted at a bulk inlet Reynolds number of Rein=2700 based on the tube radius and inlet parameters. The results demonstrate that hydraulic roughness effectively enhances heat transfer, leading to reduced wall temperatures and increased Nusselt numbers at the heated wall. As the roughness height increases, the heat transfer deterioration typically observed in SCF flows is significantly mitigated. This enhancement in heat transfer primarily arises from increased turbulent shear stress and turbulent heat flux induced by hydraulic roughness. Additionally, hydraulic roughness fosters more turbulent structures and intensifies vortex motion during transient flow, thereby further enhancing turbulent heat transfer. The insights gained from this research offer valuable guidance for addressing heat transfer deterioration in supercritical fluids.

Hybrid simulation of dissipative particle dynamics and computational fluid dynamics for friction drag reduction of polymer coatings

Frictional drag reduction (DR) can lead to substantial fuel savings in marine vehicle propulsion. The application of polymer coatings on vehicle surfaces has been found to assist in reducing drag. However, there has been limited investigation into such non-uniform polymer drag reduction in external flows. This study proposes a novel numerical model that combines a mesoscopic method with computational fluid dynamics (CFD) techniques. The CFD portion of the model uses direct numerical simulation (DNS) and large eddy simulation (LES) methods, which are verified against reference data. Firstly, the mesoscopic dissipative particle dynamics (DPD) method is coupled with DNS and LES methods, and the finitely extensible nonlinear elastic approach is used to validate the results obtained using this DNS/LES-DPD method. The performance of the model is evaluated at three representative Reynolds numbers (180, 395, and 590) to confirm its universal applicability. The model is then used to investigate the influence of the height of the polymer region on non-uniform polymer DR. Notably, the LES method offers computational savings when the Reynolds numbers are high. The model also reveals that the polymer DR efficiency is significant even when the polymer region does not extend across the entire fluid area such as the application of polymer coating. This model represents a foundation for further research on polymer coatings DR and energy conservation of vessels.