Theoretical and Computational Fluid Dynamics最新文献

In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results.

In the paper (Theoret Comput Fluid Dyn 36:705–722, 2022), we analyzed acoustic receptivity of the boundary layer on a flat plate in Mach 6 flow at various angles of attack (AoA). It was shown that slow and fast acoustic waves passing through: a bow shock at AoA(=-5^{circ }), a weak shock induced by the viscous–inviscid interaction at AoA(=0^{circ }), or an expansion fan at AoA( = 5^{circ }), excite dominant modes F and S in a small vicinity of the plate leading edge. The present paper extends this analysis to the cases of receptivity to entropy and vorticity waves. Similar to the case of acoustic receptivity, modes F and S of about equal amplitude are excited in a small vicinity of the plate leading edge. These modes propagate downstream in accord with the two-mode approximation model accounting for the mean-flow nonparallel effects and the intermodal exchange mechanism. Cross-comparisons of the initial amplitudes of excited modes help to evaluate the relative role of acoustic, entropy and vorticity waves in the second-mode dominated transition.

Reconstruction of unsteady vortical flow fields from limited sensor measurements is challenging. We develop machine learning methods to reconstruct flow features from sparse sensor measurements during transient vortex–airfoil wake interaction using only a limited amount of training data. The present machine learning models accurately reconstruct the aerodynamic force coefficients, pressure distributions over airfoil surface, and two-dimensional vorticity field for a variety of untrained cases. Multi-layer perceptron is used for estimating aerodynamic forces and pressure profiles over the surface, establishing a nonlinear model between the pressure sensor measurements and the output variables. A combination of multi-layer perceptron with convolutional neural network is utilized to reconstruct the vortical wake. Furthermore, the use of transfer learning and long short-term memory algorithm combined in the training models greatly improves the reconstruction of transient wakes by embedding the dynamics. The present machine-learning methods are able to estimate the transient flow features while exhibiting robustness against noisy sensor measurements. Finally, appropriate sensor locations over different time periods are assessed for accurately estimating the wakes. The present study offers insights into the dynamics of vortex–airfoil interaction and the development of data-driven flow estimation.

Theoretical assessments of the crossflow (CF) stabilization due to flow slip produced by small grooves on a swept supersonic wing are performed using the linear theory for inviscid flow, the local similar approximation of the boundary layer flow, the slip boundary conditions on the grooved surface and the linear stability theory. The (e^{N}) computations for stationary CF mode predict that spanwise-invariant grooves with their half-period equal to 0.25 of the boundary-layer displacement thickness can delay the CF-induced transition onset by about 10% on a (30^{circ }) swept wing having a parabolic airfoil of 5% thickness ratio, at freestream Mach number 2. It is concluded that the groove laminarization concept deserves further studies.

Perching and hovering are two bio-inspired flight maneuvers that have relevance in engineering, especially for small-scale uncrewed air vehicles. In a perching maneuver, the vehicle decelerates to zero velocity while pitching or plunging, and in hovering the pitch and plunge motion kinematics are used to generate fluid dynamic forces even when the vehicle velocity is zero. Even for an airfoil, the fluid dynamics of such maneuvers pose challenges for low-order modeling because of the time-varying freestream velocity, high amplitudes and rates of the motion kinematics, intermittent formation and shedding of the leading-edge vortex (LEV), and the strong effects of the shed vorticity on the loads. In an earlier work by the authors, a leading-edge suction parameter (LESP) was developed to predict intermittent LEV formation for round-leading-edge airfoils undergoing arbitrary variation in pitch and plunge at a constant freestream velocity. In this research, the LESP criterion is extended to situations where the freestream velocity is varying or zero. A discrete vortex method based on this criterion is developed and the results are compared against those from a computational fluid dynamics (CFD) method. Abstractions of perching and hovering maneuvers are used to validate the predictions in highly unsteady vortex-dominated flows, where the time-varying freestream/translational velocity is small in magnitude compared to other contributions to the velocity experienced by the airfoil. Time instants of LEV formation, flow features, and force coefficient histories for the various motion kinematics from the method and CFD are obtained and compared. The LESP criterion is seen to be successful in predicting the start of LEV formation, and the discrete vortex method is effective in modeling the flow development and forces on the airfoil.

We study the modal stability analysis for a three-dimensional fluid flowing over a saturated porous substrate where the porous medium is assumed to be anisotropic and inhomogeneous. A coupled system of time-dependent evolution equations is formulated in terms of normal velocity, normal vorticity, and fluid surface deformation, respectively, and solved numerically by using the Chebyshev spectral collocation method. Two distinct instabilities, the so-called surface mode instability and the shear mode instability, are identified. Modal stability analysis predicts that the Darcy number has a destabilizing influence on the surface mode instability but has a stabilizing influence on the shear mode instability. Similarly, the surface mode instability intensifies but the shear mode instability weakens with the increase in the value of the coefficient of inhomogeneity. Although the anisotropy parameter shows a stabilizing effect, increasing porosity exhibits a destabilizing effect on the shear mode instability. However, the anisotropy parameter and porosity have no significant impact on the surface mode instability. Spanwise wavenumber is found to have a stabilizing influence on both the surface mode and shear mode instabilities.

In the engineering field, it is necessary to construct a numerical model that can reproduce multiphase flows containing three or more phases with high accuracy. In our previous study, by extending the conservative Allen–Cahn (CAC) model, which is computationally considerably more efficient than the conventional Cahn–Hilliard (CH) model, to the multiphase flow problem with three or more phases, we developed the conservative Allen–Cahn type multi-phase-field (CAC–MPF) model. In this study, we newly construct the improved CAC–MPF model by modifying the Lagrange multiplier term of the previous CAC–MPF model to a conservative form. The accuracy of the improved CAC–MPF model is evaluated through a comparison of five models: three CAC–MPF models and two CH–MPF models. The results indicate that the improved CAC–MPF model can accurately and efficiently perform simulations of multiphase flows with three or more phases while maintaining the same level of volume conservation as the CH model. We expect that the improved CAC–MPF model will be applied to various engineering problems with multiphase flows with high accuracy.

The initiation of leading-edge-vortex formation in unsteady airfoil flows is governed by flow criticality at the leading edge. While earlier works demonstrated the promise of criticality of leading-edge suction in governing LEV shedding, this criterion is airfoil and Reynolds number dependent. In this work, by examining results from Navier–Stokes computations for a large set of pitching airfoil cases at laminar flow conditions, we show that the onset of flow reversal at the leading edge always corresponds to the boundary-layer shape factor reaching the same critical value that governs laminar flow separation in steady airfoil flows. Further, we show that low-order prediction of this boundary-layer criticality is possible with an integral-boundary-layer calculation performed using potential-flow velocity distributions from an unsteady panel method. The low-order predictions agree well with the high-order computational results with a single empirical offset that is shown to work for multiple airfoils. This work shows that boundary-layer criticality governs LEV initiation, and that a low-order prediction approach is capable of predicting this boundary-layer criticality and LEV initiation.

A numerical investigation of active mixing of yield stress fluids using a mixer recently proposed in El Omari et al. (Phys Rev Fluids 6(024):502, 2021. https://doi.org/10.1103/PhysRevFluids.6.024502) and tested experimentally with Newtonian fluids (Younes et al. in Int J Heat Mass Transf 187(122):459, 2022) is presented. As the Bingham number (defined by the ratio of the yield stress to the viscous stress) is increased past a critical value (text {Bn}_{textrm{bulk}}^textrm{crit}approx 5), a dramatic decrease of both the efficiency of the mixing process and of the homogeneity of the final mixture is observed. Further physical insights into this observation are obtained by a systematic analysis of the space-time dynamics of the flow fields in both Eulerian and Lagrangian frames. The numerical results show that the cascade of the passive scalar fluctuations from the wave numbers associated to the integral scale at which the passive scalar is injected down to the diffusive scale is obstructed by the emergence of a supplemental space scale associated to the characteristic size of the un-yielded material elements. The study is complemented by the discussion of two plausible solutions for alleviating the dramatic loss of mixing efficiency induced by the viscoplastic fluid behavior.

We numerically investigate the flow dynamics in a model of a dilated thoracic aorta, and compare the flow features with the case of a prosthetic replacement in its ascending part. The flow is characterized by an inlet jet which impacts the aortic walls and sweeps toward the aortic arch. Secondary flows generated by the transvalvular jet evolve downstream into a helical flow. The small curvature radius at the end of the aortic arch induces flow separation and vortex shedding in the initial part of the descending aorta, during the systole. The implantation of a prosthesis determines several modifications in the global and local flow patterns. An increase of the pulse wave velocity in the aorta leads to larger pressures inside the vessel, due to the geometrical and rigidity modifications. The sweeping jet is more aligned along the axial direction and propagates faster along the aortic arch. Consequently, a stronger separation of the flow downstream of the aortic arch is observed. By also exploiting manifold analysis, we identify regions characterized by near-wall disordered flows which may present intense accumulation and drop of concentration of biochemicals. These regions are localized downstream of the prosthetic replacement, in the aortic arch, and may be more prone to a new emergence of vessel dilation.