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Publication date: 30 June 2023
Source: Computers & Fluids, Volume 260
Author(s): Miguel Uh Zapata, Francisco J. Hernandez-Lopez, Reymundo Itzá Balam
Publication date: 30 June 2023
Source: Computers & Fluids, Volume 260
Author(s): Benigno Marco Fanni, Emanuele Gasparotti, Emanuele Vignali, Claudio Capelli, Vincenzo Positano, Simona Celi
Publication date: 30 June 2023
Source: Computers & Fluids, Volume 260
Author(s): Song Zhao, Karthik Bhairapurada, Muhammad Tayyab, Renaud Mercier, Pierre Boivin
Publication date: 30 June 2023
Source: Computers & Fluids, Volume 260
Author(s):
Publication date: Available online 19 May 2023
Source: Computers & Fluids
Author(s): Francois Delassaux, Iraj Mortazavi, Vincent Herbert, Charles Ribes
Publication date: Available online 25 May 2023
Source: Computers & Fluids
Author(s): Zhangbo Zhou, Juchun Ding, Shenghong Huang, Xisheng Luo
Publication date: 30 June 2023
Source: Computers & Fluids, Volume 260
Author(s): Weiyin Liang, Chengliang Xuan, Zhangrong Qin, Binghai Wen
Publication date: 30 June 2023
Source: Computers & Fluids, Volume 260
Author(s): Fawaz Alzabari, Catherine A.M.E. Wilson, Pablo Ouro
Publication date: 15 July 2023
Source: Computers & Fluids, Volume 261
Author(s): Peng Li, Jianqiang Chen, Mingsong Ding, Tao Jiang, Jie Mei, Yang'aoxiao Fu, Weizhong Dong
Publication date: 15 July 2023
Source: Computers & Fluids, Volume 261
Author(s): Zhangrong Qin, Wenbo Chen, Chunyan Qin, Xin Xu, Binghai Wen
With the proposed algorithm coarsely resolved gas-liquid interfaces in the multifield two-fluid model are characterized by direction of the flow relative to the interface orientation and by the dimensionless interface thickness defined in terms of the flow's shear length scale. Based on those two quantities an under-resolution indicator function is formulated. Via this information the interfacial momentum coupling is adapted to low grid resolutions in order to reduce the grid dependency of simulation results of interfacial multiphase flows.
Morphology-adaptive multiphase models are becoming more established for the numerical description of complex gas-liquid flows adapting dynamically to the local flow morphology. In the present study, two different numerical methods originally designed for distinct flow morphologies are combined, namely the volume-of-fluid and the Euler–Euler method. Both edge cases have been proven to be capable of delivering reliable predictions in the respective use cases. The long-term goal is to improve the prediction of gas-liquid flows, regardless of the flow regime in a specific application. To capture the system dynamics with a given grid resolution, the flow fields need to be predicted as precise as possible, while the shape of structures such as gas bubbles need to be recovered adequately in topology and shape. The goal is to obtain reliable predictions on intermediate mesh resolutions rather than relying on fine meshes requiring more computational resources. Therefore, a procedure is proposed to locally measure the degree of resolution. With this information, the hydrodynamics in the interface region can be controlled by means of a dedicated interfacial drag formulation in order to improve simulation results across several levels of spatial resolution. A modified formulation of buoyancy is proposed to prevent unphysical oscillations of vertical velocity near a horizontal interface. The functionality is demonstrated in a three-dimensional case of a gas bubble rising in stagnant liquid and in a co-current stratified air-water channel flow in two-dimensional space. The choice of these different applications demonstrates the general applicability of the proposed model framework.
In the present research, the Levenberg–Marquardt technique combined with backpropagated neural networks is used to assess the nanomaterial flow of the Darcy-Forchheimer Williamson nanofluid model. Results from the current study are compared with existing results, which support the validity of the present approach.
Modern industries face a new challenge in cooling processes. Traditional cooling lubricants have limited heatconducting capacity. The development of nanofluids possessing superior properties such as high thermal conductivity, homogeneity, and long-term stability has revolutionized the cooling lubrication industry. The literature reports a wide range of applications of nanofluid, such as cooling devices, peristaltic pumps for diabetic treatments, accelerators, reactors, petroleum industry applications, solar collectors and so forth. Nanofluids like Williamson nanofluid are very important non-Newtonian fluids that have pseudoplastic properties. Williamson nanofluid has a number of applications in the medical and engineering sciences. It is used in food processing, inkjet printing, adhesives and emulsions, coated photographic films, and many other applications. In the current study, the nanomaterial flow of the Darcy-Forchheimer Williamson nanofluid model is evaluated using the Levenberg–Marquardt approach with backpropagated neural networks. Thermalphoresis and Brownian motion are incorporated into the nanofluid model. This system is converted into an analogous nonlinear ordinary differential system through the application of necessary transformations. A dataset for the proposed multilayer perceptron artificial neural network is generated by altering the necessary variables through a Runge–Kutta fourth-order shooting procedure. It has been created an artificial neural network called a multiple-layer perceptron in order to forecast the values of the multiple-layer perceptron. It is discovered that the SFClss$$ {\mathrm{SFC}}_{lss} $$ parameter had the highest mean deviation of 0.26%$$ 0.26\% $$ and the LNNnlss$$ {\mathrm{LNN}}_{nlss} $$ parameter had the lowest mean deviation of −0.004%$$ -0.004\% $$. Furthermore, MSE value of ANN model developed to estimate the skin friction coefficient value as 3.55×10−05$$ 3.55\times 1{0}^{-05} $$ and R value as 0.99954 whereas MSE and R values of the ANN model developed for the estimation of the LNN value were obtained as 3.09×10−09$$ 3.09\times 1{0}^{-09} $$ and 0.99999, respectively.
A simple and efficient dry-wet boundary treatment method is proposed. We also improve difference scheme to solve the problem of distortion of left and right traveling waves propagating in the dry bed.
To solve shallow water equation, this paper proposes a simple and easy-to-operate dry-wet boundary treatment method based on the total variation diminishing (TVD)- MacCormack scheme. The method requires to judge dry and wet nodes before the calculation of prediction step and correction step, respectively. Then, the dry nodes are fictitiously celled and the topographic variables are reset. Moreover, previous researches show that when the same differential scheme was used, the left and right traveling waves showed over predicted computational fluxes during the downstream dry bed flow evolution, which led to distorted values and non-real physical phenomena. To solve the problem, the difference scheme for prediction step and correction step is modified, and a new finite difference scheme improvement method is proposed. Finally, the numerical solutions are compared with the analytical solution results by five classical cases to verify the rationality of the proposed method in this paper.
This paper investigates semi-implicit Runge-Kutta and spectral deferred correction methods up to order six for incompressible flow problems. A novel approach based on partitioned Runge-Kutta methods is proposed for embedding the projection scheme and to achieve a consistent treatment of nonlinear viscosity. Numerical experiments including laminar flow, variable viscosity and transition to turbulence demonstrate the accuracy, convergence and computational efficiency of the proposed methods and their superiority over second-order methods.
This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK) and spectral deferred correction (SDC) time-integration methods up to order six for incompressible Navier-Stokes problems in conjunction with a high-order discontinuous Galerkin method for space discretization. It is proposed to harness the implicit and explicit RK parts as a partitioned scheme, which provides a natural basis for the underlying projection scheme and yields a straight-forward approach for accommodating nonlinear viscosity. Numerical experiments on laminar flow, variable viscosity and transition to turbulence are carried out to assess accuracy, convergence and computational efficiency. Although the methods of order 3 or higher are susceptible to order reduction due to time-dependent boundary conditions, two third-order RK methods are identified that perform well in all test cases and clearly surpass all second-order schemes including the popular extrapolated backward difference method. The considered SDC methods are more accurate than the RK methods, but become competitive only for relative errors smaller than ca 10−5$$ 1{0}^{-5} $$.
The computational stability effect of multidimensional velocity components in the all-speed numerical flux scheme SLAU is investigated by comparing it with the mSLAU (formulated with only a cell interface-normal velocity component). It was observed that the multidimensional velocity components contributed to stability against poor-quality grids by isotropically producing a larger amount of numerical dissipation, especially in low-subsonic and hypersonic flows.
In computational fluid dynamics of compressible fluid flow, the simple low-dissipation advection upstream (SLAU) scheme formulated with multidimensional velocity components (normal and parallel to a cell interface) is a widely employed all-speed scheme. As a variant of SLAU, the mSLAU scheme, which adopts only a velocity component normal to the cell interface instead of multidimensional velocity components, is used for rotorcraft calculations. However, although mSLAU has been claimed to be empirically stable, it has been pointed out that using only the cell-interface-normal velocity component instead of the multidimensional velocity components causes numerical instability. Therefore, to clarify the roles of the multidimensional velocity components for computational stability, we solved some benchmark problems associated with using SLAU or mSLAU. We discovered that the multidimensional velocity components contributed to stability against poor-quality grids by isotropically producing enough amount of numerical dissipation, especially in low-subsonic and supersonic flows. Although mSLAU could practically treat moderate Mach number flows (approximately 0.1 < M < 1.0) when coupled with the minmod limiter, using only the cell-interface-normal velocity component can deteriorate convergence of calculations and lead to susceptibility in the grid geometry.
It was asserted that no multistep method with more than two steps is A-stable (Altunkaya et al. 2017). However, this article proposes a third-order multistep method that is always stable for time-dependent partial differential equations. A third-order numerical scheme has been proposed for solving parabolic equations. The scheme is linear and unconditionally stable. The comparison showed less error than the existing backward Euler scheme with fourth-order spatial discretization. The proposed scheme solves the nonlinearized partial differential equation due to the compact scheme implementation technique.
This work proposes an unconditionally stable third-order multistep technique for time-dependent partial differential equations. Its unconditional stability is proved by employing von Neumann stability analysis, and constructed Matlab code is another solid proof of the existence of the such scheme. The scheme is constructed on three consecutive time levels, and a compact fourth-order scheme is considered for spatial discretization. The convergence conditions are found when applied to the system of parabolic equations. The scheme is tested on two examples of flow between parallel plates. The mathematical model of heat and mass transfer of flow between parallel plates under the effects of viscous dissipation, thermal radiations, and chemical reaction is given and solved by the proposed scheme. The impact of some parameters, including radiation and reaction rate parameters, on velocity, temperature, and concentration profiles is also illustrated by graphs. The proposed scheme is also compared with the existing scheme, providing faster convergence than an existing one. The fundamental benefit of the proposed scheme is that it can give a compact fourth-order solution to parabolic equations.
New Findings Applying the models to practical datasets, statistics from the error analysis shows classical POD algorithm seems to be more preferred for LRA. However, since non-negativity of permeability datasets is a priority, the constrained POD (non-negative POD) algorithm described in this article is more appropriate. Results shows that the NPOD model has the capability of using minimal number of modes to reconstruct the permeability image while still retaining the geological details from the original data as opposed to the POD model.
Reservoir modeling and simulation are vital components of modern reservoir management processes. Despite the advances in computing power and the advent of smart technologies, the implementation of model-based operational/control strategies has been limited by the inherent complexity of reservoir models. Thus, reduce order models that not only reduce the cost of the implementation but also provide geological consistent prediction are essential. This article introduces reduced-order models based on the proper orthogonal decomposition (POD) coupled with linear interpolation for upscaling. First, using POD-based models, low rank approximate (LRA) are obtained by projecting the high dimensional permeability dataset to a low dimensional subspace spanned by its trajectories to decorrelate the dataset. Next, the LRA is integrated into the interpolation algorithm to generate upscaled values. This technique is highly scalable since low-rank approximations are achieved by the variation in the number of modes used for reconstruction. To test the validity and reliability of the model, we show its application to the practical dataset from SPE10 benchmark case2. From statistics of the error analysis, the classical POD algorithm seems to be more preferred for LRA; however, since non-negativity of the permeability data set is a priority, the constrained POD (non-negative POD) algorithm described in this article is more appropriate. Finally, we compared the POD-based models to a traditional industry-standard upscaling technique (e.g., arithmetic mean) to highlight our model benefits/performance. Results show that the POD-based models, particularly the non-negative POD model, produce considerably less error than the arithmetic mean model in the upscaling process.
We develop an arbitrary order finite element volume average Navier-Stokes solver that is stabilized with streamline upwind and pressure–stabilizing Petrov–Galerkin techniques and grad div stabilization. The solver is robust, globally mass conservative and supports both models A and B of the equations. Three verification cases with increasing complexity are developed using the method of manufactured solution to verify the solver while a packed bed test case is simulated to validate the solver.
The volume-averaged Navier-Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high-order finite element solver using both forms A and B of these equations. We introduce tailored stabilization techniques to prevent oscillations in regions of sharp gradients, to relax the Ladyzhenskaya–Babuska–Brezzi inf-sup condition, and to enhance the local mass conservation and the robustness of the formulation. We calculate the void fraction using the particle centroid method. Using different drag models, we calculate the drag force exerted by the solids on the fluid. We implement the method of manufactured solution to verify our solver. We demonstrate that the model preserves the order of convergence of the underlying finite element discretization. Finally, we simulate gas flow through a randomly packed bed and study the pressure drop and mass conservation properties to validate our model.
The basic idea of this article is to investigate the numerical solutions of Gardner Kawahara equation, a particular case of extended Korteweg-de Vries equation, by means of finite element method. For this purpose, a collocation finite element method based on trigonometric quintic B-spline basis functions is presented. The standard finite difference method is used to discretize time derivative and Crank–Nicolson approach is used to obtain more accurate numerical results. Then, von Neumann stability analysis is performed for the numerical scheme obtained using collocation finite element method. Several numerical examples are presented and discussed to exhibit the feasibility and capability of the finite element method and trigonometric B-spline basis functions. More specifically, the error norms L2$$ {L}_2 $$ and L∞$$ {L}_{\infty } $$ are reported for numerous time and space discretization values in tables. Graphical representations of the solutions describing motion of wave are presented.
The basic idea of this article is to investigate the numerical solutions of Gardner Kawahara equation, a particular case of extended Korteweg-de Vries equation, by means of finite element method. For this purpose, a collocation finite element method based on trigonometric quintic B-spline basis functions is presented. The standard finite difference method is used to discretize time derivative and Crank–Nicolson approach is used to obtain more accurate numerical results. Then, von Neumann stability analysis is performed for the numerical scheme obtained using collocation finite element method. Several numerical examples are presented and discussed to exhibit the feasibility and capability of the finite element method and trigonometric B-spline basis functions. More specifically, the error norms L2$$ {L}_2 $$ and L∞$$ {L}_{\infty } $$ are reported for numerous time and space discretization values in tables. Graphical representations of the solutions describing motion of wave are presented.
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s): Maria Vasilyeva
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s): Xun Wang, Hongping Guo, Zhijun Shen
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s): Changxiao Shao, Shian Yuan, Kun Luo
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s): Kirill Goncharuk, Oz Oshri, Yuri Feldman
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s): Zhiwei He, Huipo Liu, Li Li
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s): Shi Jin, Nana Liu, Yue Yu
Publication date: Available online 25 May 2023
Source: Journal of Computational Physics
Author(s): Qing Xia
Publication date: Available online 25 May 2023
Source: Journal of Computational Physics
Author(s): Hongtao Liu, Mengyu Chen, Xiaofeng Cai, Yong Cao, Giovanni Lapenta
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s):
Publication date: 15 August 2023
Source: Journal of Computational Physics, Volume 487
Author(s): G. Chen, L. Chacón
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.
This study numerically examines the influences of transverse annulation around a cone surface on the characteristics of a flow over an orthocone. This work is inspired by Spyroceras, a fossilized genus of nautiloid cephalopods from the Paleozoic era, whose method of locomotion is understudied. As a baseline case, a flow over a smooth orthoconic model with a blunt cone end is investigated numerically at Reynolds numbers from 500 to 1500. As Reynolds increases, two different shedding mechanisms—hairpin-vortex wake and spiral-vortex wake—are captured. We notice that an introduction of annulation over the cone surface changes the critical Reynolds number for the transition of the shedding mechanism. The dominant shedding frequency increases with the Reynolds number for the smooth and annulated cone flows. Moreover, the annulation reduces the dominant frequency for the same Reynolds number and increases the time-averaged drag coefficient. Modal decompositions—Proper Orthogonal Decomposition (POD) and Spectral Proper Orthogonal Decomposition (SPOD)—are used to capture the coherent structures and their oscillating frequencies. We have captured modes corresponding to the hairpin-vortex wake and spiral-vortex wake shedding mechanisms. Comparing the leading POD modes for the smooth and the annulated cone flows, we find that the annulation can reduce the twisting effects of the coherent structures in the wake. Additionally, we find that the SPOD analysis can identify modes presenting both hairpin-vortex wake and spiral-vortex wake in one flow condition as leading modes, while the POD leading modes only reveal one shedding mechanism in each flow.
This paper presents the morphological evolution characteristics of a droplet impacting a V-shaped wall by using the lattice Boltzmann method (LBM). Four parameters are investigated comprehensively. The parameters vary over wide ranges: surface wettability ( \(60^\circ \le \theta ^{eq} \le 120^\circ \) ), Weber number ( \(102.27 \le \text {We} \le 3681.82\) ), bending angle of the V-shaped wall (90 \(^\circ \le \theta \le 180^\circ \) ), and eccentricity ratio (0 \(\le b \le \) 0.5). Two types of collision are observed: deposition and breakage. For breakage, the number of satellite droplets increases against the increment of We. The splashing occurs for a high We. And the lamella ejection is observed on the hydrophilic wall and the neutral wall. The lamella ejection will be slight against the increase of \(\theta ^{eq}\) , while it will become obvious against the increment of \(\theta \) . In addition, the nondimensional spreading length, width, and height are measured and analyzed. Regime maps are established based on We, Re, and \(\theta \) .
Vortex asymmetry, dynamics, and breakdown in the wake of an axisymmetric cone have been investigated using direct numerical simulation for a wide range of angles of attack. The immersed boundary method is employed with pseudo-body-conformal grids to ensure the accuracy and resolution requirements near the body while being able to account for topology changes near the cone tip. The separated shear layer originated from the surface of the cone swirls into a strong primary vortex. Beneath the primary vortex on the leeward surface of the cone, a well-coherent counter-rotating secondary vorticity is generated. Beyond a particular threshold of swirl, the attached vortex structure breaks and the flow undergoes a chaotic transformation. Depending on the angle of attack, the flow shows different levels of instabilities and the topology of the vortices changes in the wake. In addition to swirl, spiral vortices that revolve around the primary vortex core often merge with the core and play a role in developing the double-helix mode of instability at the onset of the vortex breakdown. At the angle of attack of 60 \(^\circ \) , the time-averaged side force becomes asymmetric at the stage where the drag overcomes the lift. At the angle of attack of 75 \(^\circ \) , the primary vortex governs the flow asymmetry and the side force. Flow asymmetry is independent of the vortex breakdown. Finally, the contribution of primary vortices to the total forces is quantified using a force partitioning method.
Flow around a traveling wave-based surface-undulating NACA0012 hydrofoil has been numerically studied. In particular, we determine the effect of the phase speed of the wave, the phase difference between the waves traveling on the top and bottom surfaces, and the wave number on flow dynamics around and behind the hydrofoil and propulsive performance. The flow results in a vortex sheet or a street behind the hydrofoil, where oppositely signed vortices are aligned in either forward or reverse direction. Apart from these, side vortices start forming on either side of the hydrofoil at a higher wave number. The phase difference analysis between the upper and lower surface undulation reveals the configuration better for the hydrofoil’s lateral and longitudinal stability. The hydrofoil can shift from high thrust to high lateral force configuration by changing the phase difference between waves on the top and bottom surfaces. Thrust increases with an increase in the wave number, and a threshold value of phase speed and wave number exists where the drag-to-thrust transition happens. The added mass force-based scaling analysis corroborates with the simulated results.
A novel passive flow control strategy for the mitigation of transient separation and dynamic stall is demonstrated by means of high-fidelity large-eddy simulations. The control technique is based on a properly-sized micro-cavity cut into a wing’s underside near the leading edge, ahead of stagnation. This cavity remains essentially inactive at low incidence. However, as the wing effective angle of attack increases, the stagnation point displaces past the micro-cavity and the accelerating flow grazing the cavity induces a high-frequency resonance phenomenon or so-called Rossiter modes. The self-generated small-scale disturbances are carried around the leading-edge through the boundary layer to the wing’s upper side where the laminar separation bubble (LSB) amplifies these disturbances. This process delays LSB bursting and dynamic stall when the cavity size is selected such that its naturally occurring Rossiter modes are tuned to the receptivity of the LSB. Control effectiveness is explored for a harmonically pitching NACA 0012 wing section with freestream Mach number \(M_\infty = 0.2\) , chord Reynolds numbers \(\textrm{Re}_\textrm{c} = 5 \times 10^5\) , and maximum angle of attack of \(18^\circ \) . The flow fields are computed employing a validated overset high-order implicit large-eddy simulation (LES) solver based on sixth-order compact schemes for the spatial derivatives augmented with an eighth-order low-pass filter. Despite its simplicity, the micro-cavity resonance is found to be highly effective in preventing the deep dynamic stall experienced by the baseline airfoil. A significant reduction in the cycle-averaged drag and in the force and moment fluctuations is achieved. In addition, the negative (unstable) net-cycle pitch damping found in the baseline cases is eliminated.
