Theoretical and Computational Fluid Dynamics最新文献

We present an extension of the RSVD-(Delta t) algorithm initially developed for resolvent analysis of statistically stationary flows to handle harmonic resolvent analysis of time-periodic flows. The harmonic resolvent operator, as proposed by Padovan et al. (J Fluid Mech 900, 2020), characterizes the linearized dynamics of time-periodic flows in the frequency domain, and its singular value decomposition reveals forcing and response modes with optimal energetic gain. However, computing harmonic resolvent modes poses challenges due to (i) the coupling of all (N_{omega }) retained frequencies into a single harmonic resolvent operator and (ii) the singularity or near-singularity of the operator, making harmonic resolvent analysis considerably more computationally expensive than a standard resolvent analysis. To overcome these challenges, the RSVD-(Delta t) algorithm leverages time stepping of the underlying time-periodic linearized Navier–Stokes operator, which is (N_{omega }) times smaller than the harmonic resolvent operator, to compute the action of the harmonic resolvent operator. We develop strategies to minimize the algorithm’s CPU and memory consumption, and our results demonstrate that these costs scale linearly with the problem dimension. We validate the RSVD-(Delta t) algorithm by computing modes for a periodically varying Ginzburg–Landau equation and demonstrate its performance using the flow over an airfoil.

This paper presents simulations of dam-break flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the shallow water equations (SWE). In particular, this study aims to assess the effects of rheological parameters: power-law index (n), consistency index (K), and yield stress ((tau _{c})), on flow height and velocity over different topographies. Three practical examples of dam-break flow cases are considered: a dam-break on an inclined flat surface, a dam-break over a non-flat topography, and a dam-break over a wet bed (downstream containing an initial fluid level). The effects of bed slope and depth ratios (the ratio between upstream and downstream fluid levels) on flow behaviour are also analyzed. The numerical results are compared with experimental data from the literature and are found to be in good agreement. Results show that for both dry and wet bed conditions, the fluid front position, peak height, and mean velocity decrease when any of the three rheological parameters are increased. However, based on a parametric sensitivity analysis, the power-law index appears to be the dominant factor in dictating fluid behaviour. Moreover, by increasing the bed slope and/or depth ratio, the wave-frontal position moves further downstream. Furthermore, the presence of an obstacle is observed to cause the formation of an upsurge that moves in the upstream direction, which increases by increasing any of the three rheological parameters. This study is useful for an in-depth understanding of the effects of rheology on catastrophic gravity-driven flows of non-Newtonian fluids (like lava or mud flows) for risk assessment and mitigation.

We numerically investigate the fluidic pinball under symmetric forcing and find seven flow regimes under different rotation speeds. The fluidic pinball consists of three rotatable cylinders placed at the vertices of an equilateral triangle pointing upstream in a uniform oncoming flow. The starting point is the unforced asymmetric periodic vortex shedding at Reynolds number Re = 100 based on the cylinder diameter. The flow is symmetrically actuated by rotating the two rear cylinders at constant speed |b| up to three times the oncoming velocity in both directions. Counterclockwise (b > 0) and clockwise (b < 0) rotation of the bottom cylinder correspond to boat tailing and base bleeding, respectively. A total of seven distinct flow regimes are observed, including a steady flow, three symmetric/asymmetric periodic types of shedding, two symmetric/asymmetric quasi-periodic behaviors, and a chaotic dynamics. The vortex shedding features multiple coupled oscillator modes, including in-phase, anti-phase, and out-of-phase synchronization and non-synchronization. These shedding regimes are analyzed employing the temporal evolution of the aerodynamic forces and a dynamical mode decomposition of the wake flow. The kaleidoscope of unforced and forced dynamics promotes the fluidic pinball as a challenging modeling and control benchmark.

Shear-induced droplet formation is important in many industrial applications, primarily focusing on droplet sizes and pinch-off frequency. We propose a one-dimensional mathematical model that describes the effect of shear forces on the droplet interface evolution. The aim of this paper is to simulate paraffin wax droplets in a co-flowing fluid using the proposed model to estimate the droplet volume rate for different flow velocities. Thus, the study focuses only on the dripping regime. This one-dimensional model has a single parameter that arises from the force balance on the interface. This parameter is related to the shear layer thickness and hence influenced by the change in quantities like velocity, viscosity, and surface tension. The correlation describing the dependence of the parameter on these quantities using non-dimensional numbers is presented. The model is then cross-validated with the previous computational and experimental data. We use PETSc, an open-source solver toolkit, to implement our model using a mixed finite element discretization. We present the simulation results for liquid paraffin wax under fast-moving airflow with a range of velocities.

Employing direct numerical simulations, we investigate water and water-glycerol (85 wt%) droplets ((sim )25 µL) moving on smooth surfaces, with contact angles of around 90(^{circ }), at varying inclinations. Our focus is on elucidating the relative contribution of local viscous forces in the wedge and bulk regions in droplets to the total viscous force. We observe that, for fast-moving droplets, both regions contribute comparably, while the contribution of the wedge region dominates in slow-moving cases. Comparisons with existing estimates reveal the inadequacy of previous predictions in capturing the contributions of wedge and bulk viscous forces in fast-moving droplets. Furthermore, we demonstrate that droplets with identical velocities can exhibit disparate viscous forces due to variations in internal fluid dynamics.

We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reduced-order model (ROM) recently developed by Cavalieri and Nogueira (Phys Rev Fluids 7:102601, 2022), which considers controllability modes of the linearised Navier–Stokes system as basis functions, representing coherent structures in the flow. The velocity field is decomposed into two groups: one composed by high-controllability modes and the other by low-controllability modes. The former group is solved with the full nonlinear equations, whereas the equations for the latter are linearised. We also consider a new GQL framework wherein the linearised equations for the low-controllability modes are driven by nonlinear interactions of modes in the first group, which are characterised by large-scale coherent structures. It is shown that GQL-ROMs successfully recover the statistics of the full model with relatively high controllability thresholds and sparser nonlinear operators. Driven GQL-ROMs were found to converge more rapidly than standard GQL approximations, providing accurate description of the statistics with a larger number of linearised modes. This indicates that the forcing of linearised flow structures by large-scale coherent structures is an important feature of turbulence dynamics that should be considered in GQL models. The results presented here reveal that further model reductions are attainable with GQL-ROMs, which can be valuable to extend these models to larger Reynolds numbers.

This study presents a physics-based, low-order model for the trailing edge (TE) noise generated by an airfoil at low angle of attack. The approach employs incompressible resolvent analysis of the mean flow to extract relevant spanwise-coherent structures in the transitional boundary layer and near wake. These structures are integrated into Curle’s solution to Lighthill’s acoustic analogy to obtain the scattered acoustic field. The model has the advantage of predicting surface pressure fluctuations from first principles, avoiding reliance on empirical models, but with a free amplitude set by simulation data. The model is evaluated for the transitional flow ((text {Re} = 5e4)) around a NACA0012 airfoil at 3 deg angle of attack, which features TE noise with multiple tones. The mean flow is obtained from a compressible large eddy simulation, and spectral proper orthogonal decomposition (SPOD) is employed to extract the main hydrodynamic and acoustic features of the flow. Comparisons between resolvent and SPOD demonstrate that the physics-based model accurately captures the leading coherent structures at the main tones’ frequencies, resulting in a good agreement of the reconstructed acoustic power with that of the SPOD (within 4 dB). Discrepancies are observed at high frequencies, likely linked to nonlinearities that are not considered in the resolvent analysis. The model’s directivity aligns well with the data at low Helmholtz numbers, but it fails at high frequencies where the back-scattered pressure plays a significant role in directivity. This modeling approach opens the way for efficient optimization of airfoil shapes in combination with low-fidelity mean flow solvers to reduce TE noise.

Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust spatial support. In this context, although widely used, methods based on singular value decomposition (SVD) may produce modes that are difficult to interpret when applied to problems dominated by intermittent and transient events. Fortunately, specific modal decomposition techniques have been recently developed to analyze such problems, but a proper comparison between them is still lacking from the literature. Therefore, this work compares two recent methods: the fast adaptive multivariate empirical mode decomposition (FA-MVEMD) and the multiresolution dynamic mode decomposition (mrDMD). These techniques are employed here for the study of flow databases involving transient and intermittent dynamics. Specifically, the investigated problems include an SD7003 airfoil subjected to deep dynamic stall conditions, and a steady NACA0012 airfoil operating at a transitional Reynolds number. In the former case, the methods are employed to investigate the onset and evolution of the dynamic stall vortex (DSV), while in the latter case, intermittent vortex pairing is analyzed. We show that the combination of a multidimensional EMD with the Hilbert transform provides modes with superior spatial support when compared to the mrDMD, also allowing the characterization of instantaneous frequencies of coherent structures. Moreover, the EMD also condenses a larger amount of information within a single intrinsic mode function (IMF).

The stability of the flow past a circular cylinder in the presence of a wavy ground is investigated numerically in this paper. The wavy ground consists of two complete waves with a wavelength of 4D and an amplitude of 0.5D, where D is the cylinder diameter. The vertical distance between the cylinder and the ground is varied, and four different cases are considered. The stability analysis shows that the critical Reynolds number increases for cases close to the ground when compared to the flow past a cylinder away from the ground. The maximum critical Reynolds number is obtained when the cylinder is located in front of the waves. The wavy ground adds layers of clockwise (negative) vorticity due to flow separation from the wave peak, to the oscillating Kármán vortex. This negative vorticity from the wave peak also cancels part of the positive (counterclockwise) vorticity shed from the bottom half of the cylinder. In addition, the negative vorticity from the wave peak strengthens the clockwise (negative) vorticity shed from the top half of the cylinder. These interactions combined with the ground effect skewed the flow away from the ground. The base flow is skewed upward for all the near-ground cases. However, this skew is larger when the cylinder is located over the wavy ground. The vortex shedding frequency is also altered due to the presence of the waves. The main eigenmode found for plain flow past a cylinder appears to become suppressed for cases closer to the ground. Limited particle image velocimetry experiments are reported which corroborate the finding from the stability analysis.

An inviscid vortex shedding model is numerically extended to simulate falling flat plates. The body and vortices separated from the edge of the body are described by vortex sheets. The vortex shedding model has computational limitations when the angle of incidence is small and the free vortex sheet approaches the body closely. These problems are overcome by using numerical procedures such as a method for a near-singular integral and the suppression of vortex shedding at the plate edge. The model is applied to a falling plate of flow regimes of various Froude numbers. For (text {Fr}=0.5), the plate develops large-scale side-to-side oscillations. In the case of (text {Fr}=1), the plate motion is a combination of side-to-side oscillations and tumbling and is identified as a chaotic type. For (text {Fr}=1.5), the plate develops to autorotating motion. Comparisons with previous experimental results show good agreement for the falling pattern. The dependence of change in the vortex structure on the Froude number and its relation with the plate motion is also examined.