Flows In Complex Geometries Research Articles

Dynamic conformational response of von Willebrand factor to varying shear stress: A hybrid computational approach

This computational study examines the mechanobiological responses of von Willebrand Factor (vWF) to different shear stress levels, emphasizing the unique structural dynamics of its various domains. We introduce a novel coarse-grained model, representing each cluster of six amino acids as a bead, to synthesize the Lattice Boltzmann method with Brownian dynamics. This approach captures the vWF molecule’s conformational adaptability across a spectrum of shear rates, ranging from 5 to 5e + 7s−1, encompassing normal physiological flows to those resembling the high-shear environment of arterial stenosis.Our results reveal domain-specific responses of vWF, particularly in the A2 and A3 domains, which demonstrate significant elongation under elevated shear—reflecting their pivotal roles in clotting processes. Moreover, the study underscores the critical influence of random thermal forces on the molecule’s conformation, with simulations including these forces showing substantially greater conformational variability compared to those without.As shear rates increase, we observe a notable reorganization in the spatial arrangement of vWF domains. This reconfiguration is most evident in the increased separation between the A1 and D’D3 domains under high shear conditions, potentially enhancing the accessibility of platelets to key binding sites on vWF. These findings are paramount for a deeper understanding of vWF’s mechanical behavior in blood clotting and thrombosis, particularly the delicate balance between facilitating platelet adhesion and avoiding excessive stretching that could lead to thrombosis.Our work provides a foundation for future studies investigating vWF behavior in complex flow geometries and its interactions with other blood components. Such insights pave the way for more informed therapeutic strategies targeting vWF function in vascular health and disease, potentially leading to improved treatments for thrombotic disorders.

Bayesian reconstruction of 3D particle positions in high-seeding density flows

Abstract Measuring particles' three-dimensional (3D) positions using multi-camera images in fluid dynamics is critical for resolving spatiotemporally complex flows like turbulence and mixing. However, current methods are prone to errors due to camera noise, optical configuration and experimental setup limitations, and high seeding density, which compound to create fake measurements (ghost particles) and add noise and error to velocity estimations. We introduce a Bayesian Volumetric Reconstruction (BVR) method, addressing these challenges by using probability theory to estimate uncertainties in particle position predictions. Our method assumes a uniform distribution of particles within the reconstruction volume and employs a model mapping particle positions to observed camera images. We utilize variational inference with a modified loss function to determine the posterior distribution over particle positions. Key features include a penalty term to reduce ghost particles, provision of uncertainty bounds, and scalability through subsampling. In tests with synthetic data and four cameras, BVR achieved 95% accuracy with less than 3% ghost particles and an RMS error under 0.3 pixels at a density of 0.1 particles per pixel (ppp). This shows 57% to 97% less ghost particles and 1.3 to 2 times lower RMS error than standard MART and IPR reconstructions. In an experimental Poiseuille flow measurement, our method closely matched the theoretical solution. Additionally, in a complex cerebral aneurysm basilar tip geometry flow experiment, our reconstructions were dense and consistent with observed flow patterns. Our BVR method effectively reconstructs particle positions in complex 3D flows, particularly in situations with high particle image densities and camera distortions. It distinguishes itself by providing quantifiable uncertainty estimates and scaling efficiently for larger image dimensions, making it applicable across a range of fluid flow scenarios.

The magnetic field on the bioconvection flow of NEPCM in A Z-shaped cavity containing three circular cylinders

This work adopts an incompressible smoothed particle hydrodynamics (ISPH) method for handling the bioconvection flow of nanoparticle-enhanced phase change materials (NEPCM) inside a Z-shaped containing three circular cylinders and oxytactic microorganisms. The fractional time derivative of a system of controlling equations is solved by the ISPH method. The influences of magnetic field on thermosolutal convection of NEPCM in Z-shaped cavity. The mesh-free nature of the ISPH method helps in simulating the nanofluid flow in complex geometries. The Z-shaped cavity was chosen in this work for bioconvection flow because of its uses in semiconductors in solar cells, electronic devices, biomedicine, and thermal batteries. The bioconvection flow and heat transfer of the embedded circular cylinders are significant in heat exchangers and renewable energies. The scales of physical parameters are bioconvection Rayleigh number Rab=1−1000, Lewis number Le=1−20, Hartmann number Ha=0−80, fractional-time derivative α=0.9−1, Rayleigh number Ra=103−106, the radius of embedded circular cylinders Rc=0.05−0.2, and nanoparticles’ parameter ϕ=0−0.15. The results introduced the importance of Rab in enhancing the distributions of oxytactic microorganisms, and oxygen concentrations as well as the intensity of the velocity field. The size of embedded circular cylinders is effective in adjusting the distributions of oxytactic microorganisms, oxygen concentration, and temperature inside a Z-shaped cavity. The maximum velocity field decreases by 86.79 % as nanoparticle concentration increases from 0 % to 15 % due to the resulting high viscosity of the suspension fluid. An expanded radius of embedded circular cylinders improves the values of Nu‾ and Sh‾. This research provides crucial insights into optimizing thermal management and efficiency across diverse technological applications, from electronics to renewable energy and biomedical devices.

A mesh-free framework for high-order simulations of viscoelastic flows in complex geometries

The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable resolution for the solution of viscoelastic flows across a range of Weissenberg numbers. Based on the Local Anisotropic Basis Function Method (LABFM) of King et al. (2020), highly accurate viscoelastic flow solutions are found using Oldroyd B and PPT models for a range of two dimensional problems — including Kolmogorov flow, planar Poiseulle flow, and flow in a representative porous media geometry. Convergence rates up to 9th order are shown. Three treatments for the conformation tensor evolution are investigated for use in this new high-order meshless context (direct integration, Cholesky decomposition, and log-conformation), with log-conformation providing consistently stable solutions across test cases, and direct integration yielding better accuracy for simpler unidirectional flows. The final test considers symmetry breaking in the porous media flow at moderate Weissenberg number, as a precursor to a future study of fully 3D high-fidelity simulations of elastic flow instabilities in complex geometries. The results herein demonstrate the potential of a viscoelastic flow solver that is both high-order (for accuracy) and meshless (for straightforward discretisation of non-trivial geometries including variable resolution). In the near-term, extension of this approach to three dimensional solutions promises to yield important insights into a range of viscoelastic flow problems, and especially the fundamental challenge of understanding elastic instabilities in practical settings.

Comparison of viscoelastic flows in two- and three-dimensional serpentine channels.

Polymer solutions in the dilute regime play a significant role in industrial applications. Due to the intricate rheological properties of these highly viscoelastic fluids, especially in complex flow geometries, a thorough numerical analysis of their flow dynamics is imperative. In this research, we present a numerical investigation of purely elastic instability occurring in two- and three-dimensional serpentine channels under conditions where fluid inertia is negligible and across a broad spectrum of polymer relaxation times. Our findings reveal a strong qualitative agreement between the existing experimental results obtained from dilute solutions of flexible polymers in microfluidic devices and the numerical simulations conducted in two and three dimensions using the Oldroyd-B model. Spatial flow observations and statistical analysis of temporal flow features indicate that this purely elastic turbulent flow exhibits nonhomogeneous, non-Gaussian, and anisotropic characteristics across all scales. Additionally, our comparison of two- and three-dimensional simulations demonstrates that the elastic instability is primarily driven by the curvature of the streamlines induced by the flow geometry, rather than the weak secondary flow in the azimuthal direction. Therefore, our two-dimensional numerical simulations successfully replicate, at least qualitatively, the features observed in three-dimensional experiments. Furthermore, spectral analysis suggests that, in comparison to elastic turbulence in the dilute regime, the range of scales for the excited fluctuations is narrower.

Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes

Finding the distribution of the velocities and pressures of a fluid by solving the Navier–Stokes equations is a principal task in the chemical, energy, and pharmaceutical industries, as well as in mechanical engineering and in design of pipeline systems. With existing solvers, such as OpenFOAM and Ansys, simulations of fluid dynamics in intricate geometries are computationally expensive and require re-simulation whenever the geometric parameters or the initial and boundary conditions are altered. Physics-informed neural networks (PINNs) are a promising tool for simulating fluid flows in complex geometries, as they can adapt to changes in the geometry and mesh definitions, allowing for generalization across fluid parameters and transfer learning across different shapes. We present a hybrid quantum PINN (HQPINN) that simulates laminar fluid flow in 3D Y-shaped mixers. Our approach combines the expressive power of a quantum model with the flexibility of a PINN, resulting in a 21% higher accuracy compared to a purely classical neural network. Our findings highlight the potential of machine learning approaches, and in particular HQPINN, for complex shape optimization tasks in computational fluid dynamics. By improving the accuracy of fluid simulations in complex geometries, our research using hybrid quantum models contributes to the development of more efficient and reliable fluid dynamics solvers.

Gauging Centrifugal Instabilities in Compressible Free-Shear Layers via Nonlinear Boundary Region Equations

Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward-facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier–Stokes equations are reduced to the nonlinear boundary region equations (BREs) in a high Reynolds number asymptotic framework, wherein the streamwise wavelength of the disturbances is assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number M∞, the shear layer thickness δ, the amplitude of the incoming disturbance A, and the relative velocity difference across the shear layer ΔV on the development of these centrifugal instabilities. Our parametric study shows that, among other things, the kinetic energy of the curved shear layer flow increases with increasing ΔV and A decreases with increasing delta. It was also found that increasing the disturbance amplitude of the incoming disturbance leads to significant growth in the mushroom-like structure’s amplitude and renders the secondary instability structures more prominent, indicating increased mixing for all Mach numbers under consideration.

Quantum-inspired framework for computational fluid dynamics

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. However, the simulation of turbulent flows in complex geometries is a compute-power intensive task due to the vast vector dimensions required by discretized meshes. We present a complete and self-consistent full-stack method to solve incompressible fluids with memory and run time scaling logarithmically in the mesh size. Our framework is based on matrix-product states, a compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without passing through the expensive dense-vector representation. This framework lays the foundation for a generation of more efficient solvers of real-life fluid problems.

Thermal rarefied gas flow simulations with moving boundaries based on discrete unified gas kinetic scheme and immersed boundary method

Rarefied gas flows in complex geometries with heat transfer and moving boundaries have received remarkable attention due to the prevailing of micro/nano science and engineering applications. This study presents an immersed boundary (IB)-based discrete unified gas kinetic scheme (DUGKS) for the simulation of complex moving boundary thermal rarefied flows. The fluid and temperature fields are solved according to the DUGKS with Shakhov collision model (SDUGKS), which is capable of modeling non-unit Prandtl number problems in all Knudsen regimes. The IB approach, featured by its superior performance to incorporate complicated boundary constraints on Cartesian grids, is applied here to handling the interaction between the micro gas and curved boundaries. Specifically, for the IB adopted in this study, we use the least square method for the reconstruction of the distribution functions near the boundary. The accuracy of the IB-SDUGKS is explored comprehensively in six benchmark problems, including the micro lid-driven cavity flow, thermal equilibrium gas in a circular domain, thermal transpiration in an enclosure, moving shuttle in a rarefied gas, movement of a piston with pressure differences and particle free motion in a lid-driven cavity. The present results agree well with the corresponding analytical and direct simulation Monte Carlo (DSMC) solutions, illustrating the versatility of the present IB-SDUGKS complex thermal rarefied flows.

Implementation and assessment of a low-dissipative OpenFOAM solver for compressible multi-species flows

An ever-increasing number of engineering problems regard the numerical simulation of fluid flows with high-density ratio, shock wave onset, and different chemical species. In such conditions, obtaining reliable results depends on the ability of the numerical algorithm to offer a stable and robust time and space discretization of the governing equations while simultaneously limiting the numerical diffusivity.This work presents the extension and the assessment of a low-dissipative Navier–Stokes solver for compressible, multi-specie flows. We first studied the Richtmyer–Meshkov instability to test the code on fluid flows involving shock waves and species interactions for ideal gas. Then, we simulated a benchmark case regarding a cryogenic coaxial injector often used in rocket engines to explore the solver’s capability in representing high-Reynolds-number supercritical flows of multi-species real gases with large density gradients. Finally, we studied the flow in complex geometries like a high-pressure gasoline injector for propulsion application. The results demonstrate the capability of the present approach in the cases investigated.

A ternary phase-field model for two-phase flows in complex geometries

In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn–Hilliard model is considered as the solid phase, and only one Cahn–Hilliard equation with degenerate mobility needs to be solved due to the condition of volume conservation, which is consistent with the standard phase-field model with a single-scalar variable for two-phase flows. To depict different wetting properties at the complex fluid–solid boundaries, the spreading parameters in ternary phase-field model are determined based on the Young’s law, in which the liquid–solid surface tension coefficient is assumed to be a linear function of gas–liquid surface tension coefficient and related to the contact angle and the minimum curvature of the solid surface. In addition, to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface, the phase-field variable of the solid phase is also used to derive the modified Navier–Stokes equations. To test the present model, we further develop a consistent and conservative Hermite-moment based lattice Boltzmann method where an adjustable scale factor is introduced to improve the numerical stability, and conduct the numerical simulations of several benchmark problems. The results illustrate that present model has the good capability in the study of the two-phase flows in complex geometries.

Modeling of three-dimensional blood flow in microchannels using a two-fluid method

This work presents a novel two-fluid method based on our recently proposed viscosity model for red blood cells (RBCs)—for simulating three-dimensional (3D) blood flow in a microchannel of dimension comparable to the diameter of red blood cells and larger. Toward this, whole blood is assumed as a suspension of red blood cells in blood plasma, with each phase considered as interpenetrating continua having its separate mass and momentum conservation equations. The proposed approach-based performance study is presented after comprehensively validating it with experimental data for blood flow in a uniform, sudden expansion-constriction, and Y-shaped bifurcated rectangular microchannels over—an extensive range of size (25–330 μm), flow rates (11.8 μl/h–30 ml/h), and inlet hematocrit (0%–45%). The proposed approach effectively captures significant biophysical and biomechanical insights into blood flow. It highlights a migration of red blood cells toward the center of the microchannel and the formation of a cell-free layer near the wall. Notably, with the introduction of constriction and expansion in the microchannel, it predicts a fivefold enhancement of the cell-free layer. The Fahraeus and Fahraeus–Lindquist effects are also demonstrated in microchannels, with less than 300 μm characteristic dimensions. These findings are consistent with experimental evidence. In addition to experimentally evident phenomena, our simulations unveil several additional flow phenomena and features of blood flow in the microchannel. It is observed that the presence of confluence (merging flow) is more disturbing to the blood flow than the presence of diverging bifurcations (splitting flow). Furthermore, after the confluence, velocity profiles exhibit a local peak that persists up to the microchannel outlet. Primary contribution of this work lies in the proposal of a two-fluid method for simulating 3D blood flow in complex geometries. This approach provides a comprehensive understanding of blood flow dynamics in microchannels and can be applied to optimize dimensions and geometries during the initial phases of plasma separation microdevices development.

Data-driven turbulence modeling for fluid flow and heat transfer in peripheral subchannels of a rod bundle

This study presents a comparison of the performance of machine learning (ML) techniques, specifically multi-dimensional gene expression programming (MGEP), tensor basis neural network (TBNN), and also proposes a novel universally interpretable machine learning architecture to model the turbulent scalar flux (UIML-s) to enhance turbulence models for fluid flows at different Prandtl numbers in channels with complex shapes of walls in the channel cross section. In particular, peripheral subchannels of rod bundles are of primary interest. However, the accuracy of mean velocity and scalar distributions predicted by commonly used turbulence models still poses a challenge compared to data extracted from high-fidelity eddy-resolving numerical simulations, particularly for engineering applications involving complex geometry flows. In the present study, by utilizing an explicit algebraic expression for the nonlinear Reynolds-stress term obtained through both the evolutionary MGEP optimization and TBNN, the secondary flow structure has been adequately predicted in the cross-wise mean velocity distributions in the square duct and the rectangular channel with three longitudinal rods. This structure is also observed in the data from the concurrent runs performed by direct numerical simulation (DNS) but is completely absent in the results produced by a baseline Reynolds-averaged Navier–Stokes (RANS) closure, which employs the linear eddy viscosity model for the Reynolds stress tensor. Comparison of MGEP and TBNN has shown their nearly equal performance in a square duct flow; however, MGEP works better for the more complex geometry channel with three rods. Furthermore, based on the velocity field produced by the RANS-MGEP model, the ML modification of the gradient diffusion hypothesis, integrated into the aforementioned novel RANS-ML model called as UIML-s, significantly improves the mean scalar distributions in a flow with three bumps serving as a prototype for the peripheral subchannel of rod bundle. The normalized root mean squared error decreases from 13.5% to 7.6%, bringing the predicted distributions closer to the DNS data, particularly in the near-wall region. Another approach, MGEP-s, also yields the acceptable results, which are nearly identical to those from UIML-s. These findings highlight the potential of using data-driven calibration of turbulence models with nonlinear closures to enhance the predictability for RANS simulations of fluid flows, heat, and mass transfer in channels with complex geometry.

Numerical analysis on hydrate production performance with multi-well systems: Synergistic effect of adjacent wells and implications on field exploitation

Multi-well technology is an alternative method to achieve commercialization development of the gas hydrate, which further requires proper production strategies. However, its stimulation mechanisms remain unclear, especially the synergistic effects of adjacent wells, restricting the production strategy formulation. Thus, we established a 3D model to characterize multi-physics fields, flow characteristics, as well as productivity of hydrate reservoirs on a large scale. It can display the fluid flow in complex geometries, realizing the accurate characterization of the flow field during hydrate production with multi-well systems. Total productivity of optimal multi-well systems can be 1.44 times higher than all single wells independently, Meanwhile, physical fields and flow characteristics alter with the well position as well as well number. After that, an index Ise is proposed to realize the quantitative evaluation of the impact of synergistic effect on productivity. The impact of synergistic effect strengthens continuously versus duration time and well spacing. In addition, the occurring synergistic effect can increase productivity by promoting hydrate dissociation in expanded pressure drop areas. In contrast, the fluid resistance effect decreases the per-well produced gas and water due to inflow reduction induced by inter-well interference. Moreover, an estimation model is established to identify the proper well spacing for lower drilling costs and larger productivity. This work will enable the extended application of multi-well systems with the synergistic effect and further promote the efficient development of the gas hydrate.

Cavity flow characteristics of a curved hull section impacting a free surface with inclined postures

The water entry of structures is a complex gas–liquid flow. This paper studies the asymmetrical flow characteristics of a curved hull section entering water through numerical and experimental methods. The free-falling test from drop heights of 250–900 mm and inclination angles from 0° to 20° is carried out. Compared to a smooth hull section (cutting the bottom appendage), the experimental results observe some special asymmetrical flow phenomena (i.e., flow separation, jet impact, bubble flows, and bubble expansion). The physical mechanisms behind these flows are explained through combing the free surface flow and pressure distribution obtained by the numerical method. The effects of the inclination angle and impact velocities on these flow phenomena are further discussed, and they increase the degree of flow separation, bubble volume, and fragmentation. The load characteristics before and after cavity formation are analyzed based on a volume-of-fluid method. The high pressure caused by bubble closure can produce an instantaneous impulse pressure that even be 34% larger than the conventional impact pressure and is worth noting. This study clarifies some complex asymmetrical impact flow characteristics of curved hull sections and thus reveals the evolution mechanism of gas–liquid flows for complex geometries during oblique water entry.

Theoretical analysis of radiation effects in laminar flow over a von-Kármán body of revolution

An analysis presents the impact of thermal radiation on the laminar boundary layer established due to the motion of a von-Kármán surface. The reason for choosing such a shape is its appearance in many aeronautical vehicles, especially the F-16 fighter jet nose cone. However, the transverse curvature effects are also observable in many other shapes of bodies of revolution. But considering such a practical body of revolution provides a chance to quantify the transport phenomena happening on sophisticated aerospace vehicles. As a result, a correct understanding of the momentum and the thermal process in actual situations can be achieved. Power-law form of wall temperature is assumed to cover a variety of non-isothermal wall conditions. The typical body contour of a von-Kármán surface does not allow the scaling symmetry in the longitudinal direction; thus making the flow of non-similar in nature. An efficient numerical scheme (Keller–Box) with the second order accuracy is used for the solution purposes. The results are found to be satisfactory regarding the previous published work for moving cylinder cases. This ensures the validity of the tabulated data for the von-Kármán surface case. Through numerous tables and graphs, the impacts of thermal radiation parameter, wall temperature exponent, and transverse curvature parameter have been highlighted and thoroughly analyzed. Once the radiation parameter is increased, it is noticed that the rate of heat transfer increases and the thermal thickness of the boundary layer grows, whereas the reverse behavior is seen when the wall temperature exponent is increased. Furthermore, it has been found that increasing the surface transverse curvature increases the thermal thickness of the boundary layer and the rate of heat transfer. To the considered body shape, the reported data are expected to serve as a good source for the development of approximate methods concerning complex flow geometries involving transverse curvature effects.

Numerical investigation of heat transfer in spirally coiled corrugated pipes: Assessment of turbulence models

The Archimedean spiral coil made of a transversely corrugated pipe represents the radiant heat absorber of a parabolic dish solar concentrator. The main advantage of the considered design is the coupling of two passive methods for heat transfer enhancement: coiling the flow channel and changing the surface roughness. The aim of this numerical study is to assess the capability of RANS models of different complexity (realizable k-?, SST k-?, and RSM linear pressure-strain) to adequately represent the heat transfer phenomena in the considered complex flow geometry for wide ranges of Reynolds and Prandtl numbers. The obtained results indicate that the realizable k-? model with enhanced wall treatment is inadequate to simulate the heat transfer for all flow conditions, while both SST and RSM slightly overestimate experimental data in the turbulent region and are able to predict laminarisation at low Reynolds numbers. The SST model predictions are more accurate in the transitional and at the beginning of the turbulent region, irrespective of the curvature ratio. The RSM predictions are generally more accurate in the turbulent region. Numerically obtained circumferential distributions of local Nusselt number reveal that considered turbulence models are unable to completely anticipate the interactions between the complex flow in the basic section of the pipe and the vortex flow within the corrugations.

Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces

Flows with moving boundaries and interfaces (MBI) are a large class of problems that include fluid–particle and fluid–structure interactions, and in broader terms, moving solid surfaces. They also include multi-fluid flows, and as a special case of that, free-surface flows, sometimes in combination with moving solid surfaces. In some classes of MBI problems the solid surfaces could be in fast, linear or rotational relative motion or could come into contact. In almost all real-world applications, the solid surfaces would have complex geometries. All these problems are frequently encountered in engineering analysis and design, pose some of the most formidable computational challenges, and have a common core computational technology need. Bringing solution and analysis to them motivated the development of a good number of core computational methods and special methods targeting specific classes of MBI problems. This paper is an overview of some of those core and special methods. The focus is on isogeometric analysis, complex geometries, incompressible-flow Space–Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian–Eulerian VMS (ALE-VMS) methods, compressible-flow ST Streamline-Upwind/Petrov–Galerkin (ST-SUPG) and ALE-SUPG methods, and some of the special methods developed in connection with these core ST and ALE methods. The incompressible-flow ST-VMS and ALE-VMS and compressible-flow ST-SUPG and ALE-SUPG are moving-mesh methods, where the mesh moves to have mesh-resolution control near the fluid–solid interfaces, enabling high-resolution boundary-layer representation, an essential feature when the accuracy in representing the boundary layer is a priority. The computational examples presented are car and tire aerodynamics with road contact and tire deformation, ventricle–valve–aorta flow, and gas turbine flow.

BiGlobal stability analysis for flow in complex geometry based on immersed boundary method

A numerical framework of global stability analysis based on the immersed boundary (IB) method is established for predicting the unsteadiness onset of flow system including complex geometry. The solid wall is considered as the boundary force term and the stability analysis is applied on the orthogonal Cartesian grid, which facilitate the application of spectral collocation method in the stability analysis. To convert the linearized N-S equation with source term to homogeneous, the boundary force can be viewed as an unknown quantity, and then the no-slip boundary condition is introduced into the governing equation to close the system. The method is first tested on two canonical cases, the flow past a stationary cylinder and an isolated airfoil. The relevant results are consistent with phenomena observed in the numerical calculations and experiments, verifying the effectiveness of the method. Applying the spectral collocation method contributes to the accuracy of stability analysis and reduces the grid nodes, making it more feasible to consider complex geometry. Then, to highlight the superiority of treating the flow system with complex geometry, such as including multi-objects, the method is applied to the stability analysis of the flow past a four-square-arranged cylinder cascade. The abundant instability perturbation modes induced by the interaction of multi-objects and the corresponding relationship with the whole system are captured, which is also verified by the unsteady calculation.

Learning of viscosity functions in rarefied gas flows with physics-informed neural networks

The prediction of non-equilibrium transport phenomena in disordered media is a difficult problem for conventional numerical methods. An example of a challenging problem is the prediction of gas flow fields through porous media in the rarefied regime, where resolving the six-dimensional Boltzmann equation or its numerical approximations is computationally too demanding. A generalized Stokes phenomenological model using an effective viscosity function was used to recover rarefied gas flow fields: however, it is difficult to construct the effective viscosity function on first principles. Physics-informed neural networks (PINNs) show some potential for solving such an inverse problem. In this work, PINNs are employed to predict the velocity field of a rarefied gas flow in a slit at increasing Knudsen numbers according to a generalized Stokes phenomenological model using an effective viscosity function. We found that the AdamW is by far the best optimizer for this inverse problem. The design was found to be robust from Knudsen numbers ranging from 0.1 to 10. Our findings stand as a first step towards the use of PINNs to investigate the dynamics of non-equilibrium flows in complex geometries.