Theoretical and Computational Fluid Dynamics最新文献

An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing bias of the spectrum. Smooth spectrum estimates of broadband regions are achieved by locally reducing variance of the spectrum. The method utilizes multitaper estimation with sine tapers. An iterative criterion based on modal convergence is introduced to enable the SPOD to adapt to spectral features. For tonal flows, the adaptivity is controlled by a single user input; for broadband flows, a constant number of sine tapers is recommended without adaptivity. The discrete version of Parseval’s theorem for SPOD is stated. Proper normalization of the tapers ensures that Parseval’s theorem is satisfied in expectation. Drastic savings in computational complexity and memory usage are facilitated by two aspects: (i) sine tapers, which permit post hoc windowing of a single Fourier transform; and (ii) time-domain lossless compression using a QR or eigenvalue decomposition. Sine-taper SPOD is demonstrated on time-resolved particle image velocimetry (TR-PIV) data from an open cavity flow (Zhang et al. in Exp Fluids 61(226):1–12, https://doi.org/10.1007/s00348-020-03057-8, 2020) and high-fidelity large-eddy simulation (LES) data from a round jet (Brès et al. in J. Fluid Mech. 851:83–124, https://doi.org/10.1017/jfm.2018.476, 2018), with and without adaptivity. For the tonal cavity flow, the adaptive algorithm outperforms Slepian-based multitaper SPOD in terms of variance and local bias of the spectrum, mode convergence, and memory usage. The tonal frequencies associated with the Rossiter instability are accurately identified. For both the tonal cavity and the broadband jet flows, results comparable to or better than those from standard SPOD based on Welch’s overlapped segment averaging are obtained with up to 75% fewer snapshots, including similar convergence of the Rossiter modes and Kelvin-Helmholtz wavepacket structures for the cavity and jet examples, respectively. Drawing from these examples, we establish best practices.

This study explores coherent structures in a swirling turbulent jet. Stationary axisymmetric solutions of the Reynolds–Averaged Navier–Stokes equations at (Re=200,000) were obtained using an open source computational fluid dynamics code and the Spalart–Allmaras eddy viscosity model. Then, resolvent analysis with the same eddy viscosity field provided coherent structures of the turbulent fluctuations on the base flow. As in many earlier studies, a large gain separation is identified between the optimal and sub-optimal resolvent modes, permitting a focus on the most amplified response mode and its corresponding optimal forcing. At zero swirl, the results indicate that the jet’s coherent response is dominated by axisymmetric ((m=0)) structures, which are driven by the usual Kelvin–Helmholtz shear amplification mechanism. However, as swirl is increased, different coherent structures begin to dominate the response. For example, double and triple spiral ((|m|=2) and (|m|=3)) modes are identified as the dominant structures when the axial and azimuthal velocity maxima of the base flow are comparable. In this case, distinct co- and counter-rotating (|m|=2) modes experience vastly different degrees of amplification. The physics of this selection process involve several amplification mechanisms contributing simultaneously in different regions of the mode. This is analysed in more detail by comparing the alignment between the wavevector of the dominant response mode and the principal shear direction of the base flow. Additional discussion also considers the development of structures along the exterior of the jet nozzle.

A combined data-assimilation and linear mean-flow analysis approach is developed to estimate coherent flow fluctuations from limited mean-flow measurements. It also involves Reynolds-Averaged Navier–Stokes (RANS) modelling to efficiently tackle turbulent flows. Considering time-averaged Particle Velocimetry Image (PIV) measurements of the near-stall flow past a NACA0012 airfoil at an angle of attack of (10^{circ }) and in the chord-based Reynolds number range (4.3 cdot 10^4 le Re le 6.4 cdot 10^4), data assimilation is first employed to correct RANS equations that are closed by the Spalart-Allmaras model. The outputs of this procedure are a full mean-flow description that matches the PIV data and a consistent turbulence model that provides not only a mean eddy-viscosity field but also the perturbations of the latter with respect to mean-flow modifications. Global stability and resolvent analyses are then performed based on the so-obtained mean flow and model to satisfactorily predict near-stall low-frequency phenomena, as confirmed through comparison with the Spectral Proper Orthogonal Decomposition (SPOD) of the PIV measurements. This comparison highlights the benefits in taking into account variations in the turbulent eddy-viscosity over a frozen approach for the correct estimation of the present coherent low-frequency oscillations.

A numerical study of yield-stress fluids flowing in porous media is presented. The porous media is randomly constructed by non-overlapping mono-dispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yield-stress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence.

Fully resolved direct numerical simulations are used to quantify the effect of evolving heat, due to idealized smoldering processes, on the aerodynamic forces of a spherical particle, representing an idealized fixed-shape firebrand particle. Firebrand particles are small glowing particles that are generated in fires and can be transferred long distances by the wind and create new spot fires. Understanding the transport of firebrands is of great importance in fire science. The simulations are performed at a Reynolds number of 500, relevant for a wide range of firebrand size and wind velocity combinations. The spatiotemporal variation of temperature over the surface of the particle is obtained using a detailed surface energy balance analysis. The firebrand particle is assumed to have the thermal and material properties of pine needles and has a Biot number larger than unity, which means that the particle undergoes notable internal temperature gradients. The results indicate that the buoyancy-induced flow around the particle significantly modifies the trailing vortices and produces two non-interacting tunnel-shaped plumes in the wake of the sphere as the particle’s Richardson number increases. As a result, the particle’s drag and lift coefficients show large deviations from those of a non-heated particle and an isothermal particle. The increased surface temperatures result in an increase in the drag force while inducing a negative lift. The significant variations seen in the aerodynamic forces as a function of the particle’s instantaneous temperature indicate that the influence of the transient thermal conditions of firebrands should be considered in the prediction of the particles’ trajectory and landing spots.

Spreading time, the time that an impacting droplet attains the maximum wetting area on a solid surface, plays a critical role in many engineering applications particularly where heat transfer or chemical reactions are involved. Although the impact dynamics of a droplet significantly differ across the different spreading regimes depending on various collision parameters, it still remains unclear how the spreading time changes for each spreading regime. In the present study, the spreading time during droplet impact on a large spherical target is systematically studied at the three different spreading regimes for a wide range of impact parameters (Weber number, equilibrium contact angle, and Ohnesorge number). The changes of spreading time depending on the impact parameters and underlying physical mechanisms are analyzed in detail at the level of three different spreading regimes. Our results show that the spreading time, proper time scales, dominant impact parameters and associated physical behaviors all significantly and non-linearly change across the three spreading regimes. An improved prediction model for the spreading time is also proposed for each regime, which is now based on only the controllable variables and has an explicit form. Finally, a data-driven prediction model is proposed to represent the complicated and non-linear nature of the spreading time broadly across the three spreading regimes.

This work presents a methodology to extract coherent structures from high-speed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequency-wavenumber domain instead of the time-space domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twin-jet configuration with a small jet separation at two supersonic operation conditions: a perfectly-expanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation, together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lower-rank decomposition than schlieren-based SPOD and provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twin-jet wavepacket models available in the literature than those originally obtained with direct schlieren-based SPOD, facilitating their interpretation and comparison against theoretical analyses.

We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban et al. in J Fluid Mech 965:18, 2023).