Theoretical and Computational Fluid Dynamics最新文献

This paper presents a two-fluid model to simulate the behavior of uniformly oriented active suspensions in curved annular channels. Active suspensions consist of self-propelled particles suspended in a fluid that exhibit complex collective behavior through interactions with their surrounding environment. The proposed model captures key interactions between the fluid and particle phases, including drag and lift forces, and allows the analysis of flow patterns and particle distributions. The study investigates the flow of active suspensions in an annular channel with a rectangular cross-section, where stable secondary flow patterns develop, characterized notably by Dean vortices. Numerical simulations are used to examine the effects of channel curvature and aspect ratio on the dynamics of these suspensions. Results reveal that increased curvature intensifies the formation of Dean vortices, which significantly affect the particle distribution. Additionally, larger aspect ratios increase the strength of the secondary flow and enhance particle segregation. Model comparison to direct numerical simulations shows a qualitatively good agreement in predicting particle distribution profiles.

Controlling cavity flow through an effective magnetic field is highly desirable in many engineering applications. This work addresses the analytical solution for arbitrary depth cavity flow driven by two parallel lids under the influence of a uniform magnetic field acting along the x, y, or z axes, within the Stokes flow approximation. The formation of creeping flow and associated vortices is separated into symmetric and anti-symmetric modes, then combined to create the desired final cavity motion. The linear biharmonic equation of the stream function, modified by a Lorentz force term, is solved by constructing relevant real eigenvalues and eigenfunctions for both modes. This eigen-decomposition allows for the solution of algebraic linear equations for the coefficients in the series expansions, eliminating the need for numerical computations. This offers a significant advantage over the commonly used Papkovich-Faddle method. Our non-magnetic flow results precisely reproduce the dynamics available in the literature, primarily obtained through numerical simulations. Similarly, the MHD flow results derived from our analysis successfully replicate the numerical data found in the literature, with the exception of some ambiguous published data. These findings covering a range of Hartmann numbers between 0 and 80 valid for numerous cavity depths are further validated by finite element simulations conducted in Mathematica software, highlighting the value of the analytical solutions in discerning actual data from ambiguous information. The presented analytical solutions offer valuable physical insights into the vortical behavior of rectangular cavity motion under moderate and strong magnetic fields. The formulae clearly illustrate the breakup of the main recirculating zone, the centerline velocity structure, the core of the vortices, and the formation of boundary layers. These insights can be leveraged to determine the preferred magnetic field direction for optimal control of the cavity flow.

We present the results from a direct numerical simulation of a spanwise-periodic turbulent flow past a Gaussian bump. The problem setup is designed to investigate the interaction of an incoming turbulent boundary layer with the strong favorable and adverse pressure gradients generated by the Gaussian bump as the flow passes over it at a Reynolds number of 340000 based on the bump height, or 4 million based on the bump length. The statistical results from the present simulation are compared against our earlier results at a Reynolds number of 2 million. An internal layer, which forms beneath the strongly accelerated boundary layer over the windward side of the bump, is found to generate its near-wall turbulence stress peaks in closer proximity of the wall in the higher Reynolds-number case. Furthermore, the logarithmic layer of the higher Reynolds-number boundary layer appears more resistant to changes induced by strong acceleration and surface curvature effects over the same region. Despite a nearly identical flow separation point in the two flows, the detached shear layer grows at a faster rate and subsequently reattaches at an earlier point in the higher Reynolds-number flow. The surface pressure and skin-friction distributions over the attached flow region compare well against the corresponding experimental data for both flows. However, some differences appear in the separated flow region, which are attributed to the three-dimensionality of the experimental model setup that is not included in the simulation owing to the spanwise periodic assumption. Comparisons with the stereoscopic particle image velocimetry measurements on the central plane of the experimental model over the windward side of the bump show reasonable overall agreement in the mean velocity components, but the turbulence stress components do not agree well at some streamwise locations. Comparisons over the leeward side of the bump show that the mean separated shear layer in the simulation is tilted significantly more toward the wall than the experimental shear layer on the central plane. This mismatch in the mean shear layer orientation is due to the experimental model three-dimensionality and tunnel end-wall effects, which are not modeled in the present spanwise-periodic simulation.

When knotted or linked vortex tubes are considered in real-analytic steady Euler flows, the flows should be Beltrami flows with constant proportionality factors that have chaotic streamlines. In this study, four types of such Beltrami flows were derived on the assumption that the set of streamlines in each flow had hexagonal symmetry. Their systematic derivation was enabled by information provided via crystallography, which is applicable to spatially periodic objects not restricted to chemical materials. Invariant tori, which are stream and vortex tubes in Beltrami flows, were numerically investigated using various proportionality factors and initial points for the derived hexagonal flows. As a result, a variety of knotted or linked invariant tori were found to be arranged as atoms in hexagonal crystals. Some invariant tori were observed to form infinitely spreading chains with link structures similar to those of chain-mail-like polycatenanes in chemistry.

Numerical methods and results for computing rotating or stationary equilibria of vortex patches and sheets, some in the presence of point vortices, are presented. The methods are based on those recently developed by Trefethen and colleagues for solving Laplace’s equation in the complex plane by series and rational approximation. They share the common feature of finding the coefficients of the approximation by the fitting of boundary conditions using least-squares. Application of these methods to vortex patches requires their extension to the solution of Poisson’s and Laplace’s equation in two domains with matching conditions across the patch boundary. In the case of vortex sheets, the streamlines of the solution are computed along with the circulation density of the sheet. The use and accuracy of the methods is demonstrated by reproducing known results for equilibrium patches and vortex sheets, some having point vortices present. Several new numerical equilibrium solutions are also computed: a single straight sheet with two and four satellite point vortices respectively, and a three-sheeted structure, with the sheets emanating from a common point of rotation. New numerical solutions are also found for steady, doubly-connected vortex layers of uniform vorticity surrounding solid objects and such that the fluid velocity vanishes on the outer free boundary.

The implementation of the finite-difference method in curvilinear coordinates necessitates coordinate transformations, where violations of the Geometric Conservation Law (GCL) lead to loss of freestream preservation. This failure mechanism typically manifests as numerical instability or spurious physical artifacts in simulations. In this paper, we developed a freestream-preserving Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) to solve viscous problems on perturbed grids. The geometrically induced errors are eliminated with the satisfaction of GCL. The central difference method is used for the computation of viscous flux terms, and the least squares method is introduced to enhance the accuracy and robustness of this scheme for solving subsonic viscous problems. The results of several viscous numerical tests demonstrate the reliable freestream-preserving property of the new method compared to MUSCL.

Underwater explosions can generate substantial dynamic loads, leading to damage or failure of solid structures such as submarine pipelines. This process involves the interaction of high-pressure explosion products, water, and solid structures, characterized by transience, multi-phase interaction, and large deformations. In this study, a Lagrange mesh-free method called Smoothed Particle Hydrodynamics (SPH) is employed to establish a fluid-solid interaction (FSI) model for underwater contact explosions. The SPH discrete equations of governing equations of continuum media including fluid and solid are constructed as anti-symmetric forms based on the particle approximation technique and kernel gradient correction scheme. The equation of state is presented to describe the material response in strong interactions for the explosive, water, and solid, respectively. To simulate solid plasticity, the Johnson-Cook constitutive models are integrated into the SPH procedure to capture the behavior of large deformation and damage of metal structures. To address the issue of drastic changes in particle spacing caused by suddenly expanding gas, a modified particle regeneration technique (M-PRT) is proposed to refresh SPH particles in the gas domain according to the volume change rate. The first-order Moving Least Squares (MLS) approach is used to update the variables of refreshed particles, thus the linear variation of field variables is reproduced. The accuracy of the model is verified through several examples, including free-field underwater explosions, near-wall underwater explosions, and underwater contact explosions.

For inviscid irrotational fluid motion, the nonlinear Lagrangian equations for periodic plane acoustic waves and long gravity waves are formally similar. It then follows that the Stokes drift is similar and can be calculated for the two problems. However, the lack of dissipative processes means that the Eulerian mean current cannot be determined, and hence the acoustic streaming velocity and the Lagrangian mean surface-wave drift remain unknown. To remedy this without altering the irrotational character of the fluid motion, we add a small frictional force which is linear in the velocity, or a so-called Rayleigh friction. Then, the Lagrangian mean drift (Stokes drift (+) Eulerian current) is uniquely determined. With this assumption, the acoustic streaming velocity is (left( gamma +1 right) /2) times the Stokes drift in sound waves, where (gamma ) is the adiabatic constant. For long gravity waves, the Lagrangian mean drift is 3/2 times the Stokes drift in surface waves. These results are valid whatever small the Rayleigh friction coefficient is, as long as it is not zero.

Two-dimensional open channel flow past a rectangular disturbance in the channel bottom is considered in the case of supercritical flow, where the dimensionless flow rate is greater than unity. The response of the free surface to the height and length of a rectangular disturbance is investigated using the forced Korteweg–de Vries model of Michalski et al. (Theor Comput Fluid Dyn 38:511–530, 2024). A rich and complex structure of solutions is found as the length of the disturbance increases, especially in the case of a negative disturbance. As the length of the disturbance is decreased, some solutions approach those of the well-studied point forcing approximation, but there are other solutions, for a negative disturbance, that are not predicted by the point forcing model. The stability of steady solutions is then considered numerically with established pseudospectral methods.