Theoretical and Computational Fluid Dynamics最新文献

This article presents a macroscopic closure for rarefied polyatomic gas flows, focusing on a regularized Gaussian 11-moment (RG11) system. Our model uses a generalized Gaussian distribution-a product of Gaussian and Gamma functions-to capture both translational and internal energies of polyatomic molecules. The closure is achieved through a regularization technique, following Struchtrup & Torrilhon (Physics of Fluids, vol. 15, 2003) approach for R13 equations in monatomic gases. In addition, we use a Bhatnagar-Gross-Krook (BGK)-type relaxation model to evaluate the production terms in the moment equations. The proposed model incorporates three relaxation parameters, which can be tuned to match viscosity, bulk viscosity, and thermal conductivity accurately for the gas under consideration. By applying a Chapman-Enskog-like expansion and an order-of-magnitude analysis, we derive the RG11 equations, featuring non-zero constitutive relations for both internal and translational heat flux. This new formulation is linearly stable in one-dimensional case across all wavelengths and frequencies, aligns well with experimental data for sound wave propagation, and agrees with validated hydrodynamic theories that are known to match experimental results for Rayleigh-Brillouin scattering (RBS), outperforming the Navier-Stokes-Fourier (NSF) equations.

The current study introduces a novel fully coupled monolithic solver for the direct forcing immersed boundary method (IBM) in incompressible flows. The solver simultaneously integrates pressure, velocity, nonlinear convection terms, and Lagrangian forces into a unified framework, leveraging a modified big-box Vanka smoother extended with additional Lagrange multipliers arising from the IBM formulation. Central to the approach is the use of a Schur complement decomposition, which reduces the operator size by two-thirds while preserving both stability and accuracy. The solver’s monolithic structure eliminates splitting errors and artificial pressure boundary conditions, common drawbacks of segregated methods. Additionally, the developed methodology enables high CFL numbers (up to 0.5), making it particularly effective for moving boundary simulations. Verification studies cover a broad set of benchmark problems, including both stationary and moving immersed bodies across a wide range of Reynolds numbers. These tests confirm that the solver achieves computational times comparable to existing semi-implicit methods while enhancing accuracy and stability. By addressing key challenges in high-fidelity incompressible flow simulations, the proposed method offers a robust and broadly applicable monolithic solver.

The study of peristaltic Eyring-Powell nanofluid (EPF) with microorganisms is crucial in biomedical and industrial processes, improving drug delivery systems, bioreactors, and targeted microorganism transport. The EPF in a curved peristaltic channel under the influence of a uniform normal magnetic field (MF) and inside a permeable material is therefore considered in the current issue. The flow also comprises microorganisms and is motivated by the effects of porous media, Joule heating, non-Newtonian dissipation, and chemical reactions. The current work innovation stems from the inclusion of nanoparticles and microorganisms through non-Newtonian fluid flows in a curved channel, utilizing the curvilinear coordinates, which have several implications in engineering, industry, and biology. The flow under contemplation is caused by peristaltic waves that have a constant wavelength and amplitude. The problem’s governing equations are modeled using curvilinear coordinates. The goal is to maintain simplicity, and subsequently, so the problem is illustrated in the wave frame instead of the fixed frame. Under low Reynolds number and long wavelength approximation in the wave frame of reference, the mathematical framework addresses energy, momentum, nanomaterial’s volume fraction, and microbe concentration together with appropriate boundary conditions (BCs). The solutions of the governing system are handled with the help of shooting criteria and an appropriate numerical implicit method via the fourth-order Runge-Kutta (RK-4). The physical outcomes concerning flow parameters are presented to indicate the enhancement and decay factors of all relevant distributions, together with the heat and mass transfer coefficients. It is found that the factors that enhance the existence of nanoparticles and heat broadcast are the same that decay the presence of microbes, which gives practical importance to the current issue.

The study here is of two-dimensional constricted channel flows and insight into their properties as the degree of constriction varies. This is potentially helpful for a range of applications as well as being of basic scientific interest. Two main computational approaches are taken, one via direct numerical simulation of the Navier-Stokes equations, and the other in the large Reynolds number limit where the boundary layer equations apply wall-to-wall. The focus is on understanding more of, and quantifying, the relatively unknown effects of wall icing in channel flow of water, as well as making quantitative comparisons between solutions from the two computational approaches and similar comparisons with recent work on the melting of wall-mounted ice. Flow separation, eddy lengths, pressure responses for sufficiently constricted internal vessels and upstream or downstream influence are examined. The retention of the ice when undercooling is present at the vessel wall is also studied. Severe blocking followed by eventual mild blocking or complete unblocking of the water flow is commonly found.

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.