Theoretical and Computational Fluid Dynamics最新文献

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.

This paper investigates the effect of permeability on two-dimensional rectangular plates at incidences. The flow topology is investigated for Reynolds number (Re) values between 30 and 90, and the forces on the plate are discussed for (Re=30), where the wake is found to be steady for any value of the Darcy number (Da) and the flow incidence ((alpha )). At (Re=30), for a plate normal to the stream and vanishing Da, the wake shows a vortex dipole with a stagnation point on the plate surface. With increasing Da, the separation between the vortex dipole and the plate increases; the vortex dipole shortens and is eventually annihilated at a critical Da. For any value of Da below the critical one, the vortex dipole disappears with decreasing (alpha ). However, at low Da, the two saddle-node pairs merge at the same (alpha ), annihilating the dipole; while at high Da, they merge at different (alpha ), resulting in a single recirculating region for intermediate incidences. The magnitudes of lift, drag, and torque decrease with Da. Nevertheless, there exists a range of Da and (alpha ), where the magnitude of the plate-wise force component increases with Da, driven by the shear on the plate’s pressure side. Finally, the analysis of the fluid impulse suggests that the lift and drag reduction with Da are associated with the weakening of the leading and trailing edge shear layer, respectively. The present findings will be directly beneficial in understanding the role of permeability on small permeable bodies.

The spread of machine learning techniques coupled with the availability of high-quality experimental and numerical data has significantly advanced numerous applications in fluid mechanics. Notable among these are the development of data assimilation and closure models for unsteady and turbulent flows employing neural networks (NN). Despite their widespread use, these methods often suffer from overfitting and typically require extensive datasets, particularly when not incorporating physical constraints. This becomes compelling in the context of numerical simulations, where, given the high computational costs, it is crucial to establish learning procedures that are effective even with a limited dataset. Here, we tackle those limitations by developing NN models capable of generalizing over unseen data in low-data limit by: (i) incorporating invariances into the NN model using a Graph Neural Networks (GNNs) architecture; and (ii) devising an adaptive strategy for the selection of the data utilized in the learning process. GNNs are particularly well-suited for numerical simulations involving unstructured domain discretization and we demonstrate their use by interfacing them with a Finite Elements (FEM) solver for the supervised learning of Reynolds-averaged Navier–Stokes equations. We consider as a test-case the data-assimilation of meanflows past generic bluff bodies, at different Reynolds numbers (50 le Re le 150), characterized by an unsteady dynamics. We show that the GNN models successfully predict the closure term; remarkably, these performances are achieved using a very limited dataset selected through an active learning process ensuring the generalization properties of the RANS closure term. The results suggest that GNN models trained through active learning procedures are a valid alternative to less flexible techniques such as convolutional NN.