Theoretical and Computational Fluid Dynamics最新文献

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.

Normal shock trains are a flow phenomenon of significance to ramjet engines, but it remains unclear what its structure is decided by and how it evolves with the incoming Mach number. To seek a theoretical explanation, the minimum entropy production principle is generalized to the quasi-steady behavior of normal shock trains in two-dimensional straight channels with uniform incoming flow. Numerical simulations are also performed to validate the model together with the data collected from public literature. The analysis suggests that the flow parameters of a normal shock train depend on the inviscid shock-shock interactions rather than the local boundary-layer separations, though the angles of two incident shocks should still be equal as similar to the case that complies with the free-interaction theory. The shock feet’s positions, meanwhile, are allowed to be coincident or not, free from the entropy restriction. This freedom of position explains why both symmetric and partially asymmetric normal shock trains could be found previously. Further theoretical calculations reveal the inclinations of two incident shocks increase first and then decrease with the incoming Mach number, peaking at 48.570 degrees when the Mach number reaches 1.753. It is also indicated that the Mach number range allowing for a normal shock train is 1.652 to 2.254, giving evidence for past observations.

A numerical approach is proposed for the study of instabilities in helical vortex systems as found in the near-wake of turbines or propellers. The methodology has a high degree of generality, yet the present paper focusses on the case of one unique helical vortex. First, a method based on helical symmetry aimed at computing a three-dimensional base flow with prescribed parameters—helical pitch, helical radius, vortex circulation, core size and inner jet component—is presented. Second, the linear instability of this base flow is examined by reducing the three-dimensional instability problem to two-dimensional simulations with wavenumbers prescribed along the helix axis. Each simulation converges towards an exponentially growing or decaying complex state from which eigenfunctions, growth rate and frequency are extracted. This procedure is validated against a standard method based on direct three-dimensional numerical simulations of the Navier–Stokes equations linearized in the vicinity of the same helical base flows. Three illustrative base flows are presented with or without inner jet component, the instability of which is dominated, at the prescribed axial wavenumber, by unstable modes of three different types: long-wave instability, short-wave elliptic and curvature instabilities. Results from the new procedure and from the fully three-dimensional one are found in excellent agreement, which validates the new methodology. The gain in computational time is typically the one that is achieved while going from three-dimensional to two-dimensional simulations.