Theoretical and Computational Fluid Dynamics最新文献

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.

We apply data-driven techniques to construct a nonlinear 3-mode model of a Kolmogorov-like flow transitioning from steady to periodic. Data from direct numerical simulation that include features of experimental realizations of Kolmogorov-like flow are used to build the model. Our low-order modeling methodology does not require knowledge of the underlying governing equations. The 3-mode basis for the model is determined solely from data and the sparse identification of nonlinear dynamics framework (SINDy) is used to fit a dynamical system describing modal interactions. We impose constraints within the SINDy framework to ensure the resulting model will possess energy-preserving nonlinear terms that are consistent with the underlying flow physics. We use the low-order model to determine an appropriate equilibrium solution to stabilize, thereby avoiding searching for equilibrium solutions in the full-order system. The model is linearized about the identified equilibrium solution and subsequently used to design feedback controllers that successfully suppress an oscillatory instability when applied in direct numerical simulations—a testament to the model’s ability to capture the underlying dynamics that are most relevant for flow control. Our results confirm that low-order models obtained in a purely data-driven framework can be implemented for flow control in experimentally-realizable Kolmogorov-like flow.

We design a nonlinear estimator for channel flows at (Re_{tau }=180) and 590. The nonlinear estimator uses a linear estimator structure based on the linearised Navier–Stokes equations and explicitly calculates the nonlinear forcing from the estimated velocities in physical space. The goal is to use limited velocity measurements to predict the velocity field at other locations. We first use the velocities at one wall-normal height to estimate the velocities at other wall-normal heights. The estimation performance is compared among the nonlinear estimator, the linear estimator and the linear estimator augmented with eddy viscosity. At (Re_{tau }=180), the nonlinear estimator and the linear estimator augmented with eddy viscosity outperform the linear estimator in terms of estimating the velocity magnitudes, structures and energy transfer (production, dissipation and turbulent transport) across the channel height. The limitations of using measurement data at one wall-normal height are discussed. At (Re_{tau }=590), the nonlinear estimator does not work well with only one measurement plane, whereas the linear estimator augmented with eddy viscosity performs well. The performance of the nonlinear estimator and the linear estimator augmented with eddy viscosity at (Re_{tau }=590) is significantly enhanced by providing multiple measurement planes.

A noise modelling approach is proposed for bluff body wakes such as flow over a cylinder, where the primary noise source comprises large-scale coherent structures such as the vortex shedding flow feature. This phenomenon leads to Aeolian tones in the far-field, and is inherent in wake flows across a range of Reynolds numbers (Re), from low-Re to high-Re turbulent flows. The approach employs linear global stability analysis on the time-averaged mean flow, with amplitude calibration through two-point statistics, and far-field noise calculations from the global mode fluctuations by Curle’s analogy. The overall approach is tested for flow over a cylinder at Reynolds numbers Re = 150 and 13,300. For Re = 150 flow, noise directivity calculations from the present approach agree with direct far-field computations. For Re = 13,300 flow, the mean flow is obtained by particle image velocimetry (PIV). The linear global mode for spanwise-homogeneous-type fluctuations is obtained at the main, lift fluctuation frequency. Calibration of this global mode involves time-resolved PIV data in the streamwise-spanwise plane, which is Fourier transformed in frequency-spanwise wavenumber space. The noise calculations for this global mode are then found to be less than 1 dB off from the microphone measurements.