Viscous and inviscid interactions of an oblique shock with a flexible panel

The complex self-sustained oscillations arising from the interaction of an oblique shock with a flexible panel in both the inviscid and viscous regimes have been investigated numerically. The aeroelastic interactions are simulated using either the Euler or the full compressible Navier–Stokes equations coupled to the nonlinear von Karman plate equations. Results demonstrate that for a sufficiently strong shock limit-cycle oscillations emerge from either subcritical or supercritical bifurcations even in the absence of viscous separated flow effects. The critical dynamic pressure diminishes with increasing shock strength and can be much lower than that corresponding to standard panel flutter. Significant changes in panel dynamics were also found as a function of the shock impingement point and cavity pressure. For viscous laminar flow above the panel without a shock, high-frequency periodic oscillations appear due to the coupling of boundary-layer instabilities with high-mode flexural deflections. For a separated shock laminar boundary layer interaction, non-periodic self-excited oscillations arise which can result in a significant reduction in the extent of the time-averaged separation region. This finding suggests the potential use of an aeroelastically tailored flexible panel as a means of passive flow control. Forced panel oscillations, induced by a specified variable cavity pressure underneath the panel, were also found to be effective in reducing separation. For both inviscid and viscous interactions, the significant unsteadiness generated by the fluttering panel propagates along the complex reflected expansion/recompression wave system.     

An analytic approximate approach for free oscillations of self-excited systems

A new analytic approximate technique for non-linear problems, namely the homotopy analysis method, is employed to propose an approach for free oscillations of self-excited systems. Different from perturbation methods on this topic, this approach does not depend upon any small/large parameters at all and therefore is valid for free oscillations of all self-excited systems. Besides, unlike other analytic techniques, this approach provides us with a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. Two examples are employed to illustrate the validity and flexibility of this approach.     

Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex shedding

High-frequency limit-cycle oscillations of an airfoil at low Reynolds number are studied numerically. This regime is characterized by large apparent-mass effects and intermittent shedding of leading-edge vortices. Under these conditions, leading-edge vortex shedding has been shown to result in favorable consequences such as high lift and efficiencies in propulsion/power extraction, thus motivating this study. The aerodynamic model used in the aeroelastic framework is a potential-flow-based discrete-vortex method, augmented with intermittent leading-edge vortex shedding based on a leading-edge suction parameter reaching a critical value. This model has been validated extensively in the regime under consideration and is computationally cheap in comparison with Navier–Stokes solvers. The structural model used has degrees of freedom in pitch and plunge, and allows for large amplitudes and cubic stiffening. The aeroelastic framework developed in this paper is employed to undertake parametric studies which evaluate the impact of different types of nonlinearity. Structural configurations with pitch-to-plunge frequency ratios close to unity are considered, where the flutter speeds are lowest (ideal for power generation) and reduced frequencies are highest. The range of reduced frequencies studied is two to three times higher than most airfoil studies, a virtually unexplored regime. Aerodynamic nonlinearity resulting from intermittent leading-edge vortex shedding always causes a supercritical Hopf bifurcation, where limit-cycle oscillations occur at freestream velocities greater than the linear flutter speed. The variations in amplitude and frequency of limit-cycle oscillations as functions of aerodynamic and structural parameters are presented through the parametric studies. The excellent accuracy/cost balance offered by the methodology presented in this paper suggests that it could be successfully employed to investigate optimum setups for power harvesting in the low-Reynolds-number regime.     

An improved nonlinear reduced-order modeling for transonic aeroelastic systems

In this study, an improved nonlinear reduced-order model composed of a linear part and a nonlinear part is explored for transonic aeroelastic systems. The linear part is identified via the eigensystem realization algorithm and the nonlinear part is obtained via the Levenberg–Marquardt algorithm. The impulsive signal is chosen as the training signal for the linear part and the sinusoidal signal is used to determine the order of the linear part. The training signal for the nonlinear part is selected as the filtered white Gaussian noise with the maximal amplitude and frequency range to be designed via the aeroelastic responses. An NACA64A010 airfoil and an NACA0012 airfoil are taken as illustrative examples to demonstrate the performance of the presented reduced-order model in modeling transonic aerodynamic forces. The aeroelastic behaviors of the two airfoils are obtained via computational fluid dynamics to solve the Euler equation and the Navier–Stokes equation, respectively. The numerical results demonstrate that the presented reduced-order model can successfully predict the nonlinear aerodynamic forces with and without viscous flows. Moreover, the presented reduced-order model is capable of capturing the flutter velocity and modeling complex aeroelastic behaviors, including limit-cycle oscillations, beat phenomena and nodal-shaped oscillations at the transonic Mach numbers with high accuracy.     

Coupled framework for limit-cycle oscillations modeling based on leading-edge vortex shedding

Current trends in the aircraft industry involve higher aspect-ratio wings made of lighter materials. These trends seek to reduce fuel emissions and increase flight efficiency by reducing drag to lift ratio and overall weight, respectively, of the aircraft. This results in reduced structural stiffness and coupling between the aeroelastic modes and flight dynamics. The flutter phenomenon is of particular interest for aeroelastic studies, and modeling post-flutter limit-cycle oscillations (LCO) is a challenging problem.Several studies have been developed to allow fast simulations of the highly non-linear aerodynamic situations, with leading-edge vortex modulation been a proved solution for modeling some forms of LCOs in airfoils. This article proposes a framework based on the 3D expansion of this method using strip theory and coupling with modal structural model for simulations of aerodynamic based non-linear phenomenon. A cantilevered flat plate is used for testing and validating the framework against wind-tunnel experiments and the industry standard approach. The results show that the proposed model is able to capture the main behavior of the LCO observed in the experiments and is directly comparable with the current approaches used at the industry. The framework allows for scalability and is also fast enough to provide time-based results in under two days for a desktop simulation, reducing the need of expensive cluster computations. Finally, since it is completely physics-based it allows for the engineer to get insights on the aerodynamic flow at a fraction of the cost of more detailed CFD models.     

Rapid evaluation of the fatigue limit in composites using infrared lock-in thermography and acoustic emission

Fatigue limit determination via the conventional Wöhler-curve method is associated with extended experimental times as it requires testing of a large number of specimens. The current paper introduces a methodology for fast, reliable and experimentally economic determination of the fatigue limit in monolithic and composite materials by means of combined usage of two nondestructive inspection methods, namely infrared (IR) lock-in thermography and acoustic emission (AE). IR thermography, as a real-time and non-contact technique, allowed the detection of heat waves generated due to thermo-mechanical coupling as well as of the energy dissipated intrinsically during dynamic loading of the material. AE, on the other hand, was employed to record the transient waves resulting from crack propagation events. Aluminum grade 1050 H16 and cross-ply SiC/BMAS ceramic matrix composites were subjected to fatigue loading at various stress levels and were monitored by an IR camera and AE sensors. The fatigue limit of the monolithic material, obtained by the lock-in infrared thermography technique and supported by acoustic emission was found to be in agreement with measurements obtained by the conventional S–N curve method. The fatigue limit of the ceramic matrix composite was validated with acoustic emission data.     

Numerical study of flow-induced oscillations of two rigid plates elastically hinged at the two ends of a stationary plate in a cross-flow

The flow-induced oscillation (FIO) of bluff bodies is commonly encountered in the fluid structure interaction (FSI) problems. In this study, we use an unstructured moving grid strategy and simulate the FIO of two rigid plates, which are elastically hinged at the two ends of a fixed flat plate in a cross-flow. We use a hybrid finite-element-volume (FEV) method in an arbitrary Lagrangian–Eulerian (ALE) framework to study FIO of the two hinged plates. The current simulations are carried out for wide ranges of flow Reynolds number (50–175), spring stiffness coefficient, and the two hinged plates' moment of inertia magnitudes. The influences of these parameters are investigated on the magnitudes of maximum deflection angle, the amplitude of oscillation, the total lift and drag coefficients, and so on. The study is also carried out in the transition period to describe the in-phase and out-of-phase angular oscillations occurring for the two elastically hinged plates with respect to each other. After the transition period, the two hinged plates eventually arrive to a similar periodic oscillation; however, with some phase lags. We find that the achieved phase lag is equal to the phase lag between the two pairs of flow vortices, which are alternatively shed into the flow from the upper and lower hinged plates. Similar to past FIO problems, the current model also exhibits two important lock-in and phase-switch FSI phenomena; however, in angular directions. There is a phase jump of approximately 170° between the aerodynamic lift coefficient and angular oscillations of hinged plates, which nearly occurs in the middle of lock-in region. Indeed, our literature review shows that this is the first time to report the phase-switch phenomenon in angular oscillations of three-element bluff bodies in a FSI problem.     

弯度翼型大迎角时分离涡流场的多平衡态现象

基于kω的SST两方程湍流模型,在时间域求解雷诺平均Navier-Stokes方程,模拟弯度翼型大迎角时的分离流动。通过给翼型施加一定形式的扰动,重点关注了翼型弯度对大迎角分离涡流场平衡态转移的影响。研究结果表明:与相同厚度20%以上的对称翼型相比,2%弯度的翼型出现分离涡流场平衡态转移的起始迎角变小2°左右,迎角区间变宽约1°;在厚度相对较小的NACA2416翼型上也发现上述分离涡平衡态转移现象。由此说明翼型弯度在一定程度上促使了分离涡平衡态的转移。     

Parametric excitations and lock-in of flexible hydrofoils in two-phase flows

This work introduces a reduced-order method to study the parametric excitations and lock-in of flexible hydrofoils caused by unsteady two-phase (cavitating) flow. The reduced-order method is based on a 1-DOF structural model coupled with a van der Pol wake oscillator with empirically derived relations for the variation in lift, cavity-length, and cavity-shedding frequency as a function of a non-dimensional cavitation parameter. The results are compared with several available data from both numerical simulations and experimental measurements. The frequency content of both the predicted and measured vibrations suggested that, in addition to the primary cavity-shedding frequency and the hydrofoil natural frequencies, unsteady two-phase flows may excite additional modulated frequencies due to time-varying fluid-added mass effects. The results show that these frequency modulations might cause the flexible hydrofoil to undergo higher-order resonances, as well as parametric resonances. While the maximum deformations for the primary and higher-order resonances were observed to damp out, parametric resonances might persist even with realistic fluid damping coefficients (4–12%). It was observed that with higher effective foil flexibility, the cavity-shedding frequencies may be significantly modified from the rigid foil trends, and may instead lock-in with the system natural frequencies.     

Boundary linear integral method for compressible potential flows

A boundary linear integral method based on Green function theory has been developed to solve the full potential equation for subsonic and transonic flows. In this integral method, potential values in the flow region are determined by potential values represented by boundary integrals and a volume integral. The boundary potential values are obtained by implementing the boundary integrals along boundary segments where a linear potential relation is assumed. The volume integral is evaluated in a grid generated by finite element discretization. The volume integral is evaluated only outside the body. Therefore there is no extra boundary treatment required for evaluation of the volume integral. The source term is assumed to be constant in an element integral volume. The volume integral needs to be evaluated only once and can be stored in computer memory for further usage.     

Explicit algebraic Reynolds stress model for shock-dominated flows

Shock waves drastically alter the nature of Reynolds stresses in a turbulent flow, and conventional turbulence models cannot reproduce this effect. In the present study, we employ explicit algebraic Reynolds stress model (EARSM) to predict the Reynolds stress anisotropy generated by a shockwave. The model by Wallin and Johansson (2000) is used as the baseline model. It is found to over-predict the post-shock Reynolds stresses in canonical shock turbulence interaction. The budget of the transport equation of Reynolds stresses computed using linear interaction analysis shows that the unsteady shock distortion mechanism and the pressure–velocity correlations are important. We propose improvement to the baseline model using linear interaction analysis results and redistribute the turbulent kinetic energy between the principle Reynolds stresses. The new model matches DNS data for the amplification of Reynolds stresses across the shock and their post-shock evolution, for a range of Mach numbers. It is applied to oblique shock/boundary-layer interaction at Mach 5. Significant improvements are observed in predicting surface pressure and skin friction coefficient, with respect to experimental measurements.     

Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake

This paper describes flow around a pair of cylinders in tandem arrangement with a downstream cylinder being fixed or forced to oscillate transversely. A sinusoidal parietal velocity is applied to simulate cylinder oscillation. Time-dependent Navier-Stokes equations are solved using finite element method. It is shown that there exist two distinct flow regimes: ‘vortex suppression regime’ and ‘vortex formation regime’. Averaged vortex lengths between the two cylinders, pressure variations at back and front stagnant points as well as circumferential pressure profiles of the downstream cylinder are found completely different in the two regimes and, thus, can be used to identify the flow regimes. It is shown that frequency selection in the wake of the oscillating cylinder is a result of non-linear interaction among vortex wakes upstream and downstream of the second cylinder and its forced oscillation. Increasing cylinder spacing results in a stronger oscillatory incident flow upstream of the second cylinder and, thus, a smaller synchronization zone.     

Skin friction and heat transfer in rapidly oscillating boundary layers

The influence of rapid oscillations in the outer part of a boundary layer upon the time-averaged skin friction and heat transfer is investigated analytically. The oscillations are taken to be harmonic. The only restriction on the oscillation amplitude is that it should be sufficiently small to permit the use of the boundary layer equations. The derived asymptotic formulae show the explicit dependence of momentum transfer on the frequency and the time-averaged boundary layer flow. For the heat transfer similar formulae can be derived in a number of limiting cases, viz. when the Prandtl number is either large or small.     

格栅-空腔自激振荡流场扰动形成机理研究

格栅-空腔流动会引发流场自激振荡现象,产生结构振动及噪声问题.研究此类现象的形成机理对相关设备的减振降噪设计具有重要意义.目前已知这种现象是在流场正逆向两种扰动的耦合作用下形成的,但上述两种扰动的形成机理尚未明确.针对该问题,建立了格栅-空腔流动数值模型,并进行非稳态数值模拟.通过分析压力振荡数据及流场结构演化过程,对...     

Parametric investigation of particle acceleration in high enthalpy conical nozzle flows for coating applications

A modified cold gas-dynamic spray technique is under development by using shock tunnel technology, which can enhance the coating quality by increasing the solid particle velocity up to 1,500 m/s. The particle diameter typically amounts to 10 μm. A theoretical model based on gas-particle flows is employed to describe the behaviour of the flow and the solid particles. This quasi-1D model is capable to consider non-equilibrium effects of the gas phase due to high reservoir temperatures, and the influence of wall friction and heat transfer averaged over the nozzle cross section. This model is used for the design and optimization of the nozzle geometry by a parametric study, which results in a conical nozzle with a half opening angle of 2.8° and a length of 325 mm. Particles for coating are injected at about 55 mm downstream of the throat. A shock tunnel facility has been set up at the Shock Wave Laboratory for performing an experimental study of this new technique. The theoretical performance of this setup is evaluated by the KASIMIR simulation software and the quasi-1D method described in this paper. The high reservoir conditions required to achieve particle velocities of 1,500 m/s can be realized by using either a very high driver pressure of about 600 bar for air as driver gas or a relatively low driver pressure of about 200 bar for helium as driver gas.      

Time domain simulation of vortex-induced vibrations in stationary and oscillating flows

This paper focuses on the further development of a previously published semi-empirical method for time domain simulation of vortex-induced vibrations (VIV). A new hydrodynamic damping formulation is given, and the necessary coefficients are found from experimental data. It is shown that the new model predicts the observed hydrodynamic damping in still water and for cross-flow oscillations in stationary incoming flow with high accuracy. Next, the excitation force model, which is one component of the total hydrodynamic force model, is optimized by simulating the VIV response of an elastic cylinder in a series of experiments with stationary flow. The optimization is performed by repeating the simulations until the best possible agreement with the experiments is found. The optimized model is then applied to simulate the cross-flow VIV of an elastic cylinder in oscillating flow, without introducing any changes to the hydrodynamic force modeling. By comparison with experiment, it is shown that the model predicts the frequency content, mode and amplitude of vibration with a high level of realism, and the amplitude modulations occurring at high Keulegan–Carpenter numbers are well captured. The model is also utilized to investigate the effect of increasing the maximum reduced velocity and the mass ratio of the elastic cylinder in oscillating flow. Simulations show that complex response patterns with multiple modes and frequencies appear when the maximum reduced velocity is increased. If, however, the mass ratio is increased by a factor of 5, a single mode dominates. This illustrates that, in oscillating flows, the mass ratio is important in determining the mode participation at high maximum reduced velocities.     

Calculation of the unsteady aerodynamic parameters of a rotating cascade of oscillating blades in incompressible flow

The unsteady aerodynamic parameters of 3D blade cascades oscillating in incompressible flow are determined with account for blade geometry and the influence of the steady hydrodynamic loads acting on the blades. On the assumption of separationless flow and harmonic blade oscillations, the corresponding boundary-value problem for the amplitude function of the unsteady velocity potential component is solved in the linear formulation, using a finite-element method. Test calculation results are presented and an example of calculating the unsteady aerodynamic parameters of a hydro-turbine model is given.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 40–52. Original Russian Text Copyright © 2005 by Kurzin and Tolstukha.     

Numerical investigations on the dynamic behavior of a 2-DOF airfoil in the transitional Re number regime based on fully coupled simulations relying on an eddy-resolving technique

The paper is the numerical counterpart of the experimental investigation on the fluid–structure interaction (FSI) of a wing with two degrees of freedom (DOF), i.e., pitch and heave. Wood et al. (2020) has provided the experimental basis by studying the flutter stability of an elastically mounted straight wing (NACA 0012 airfoil) in a wind tunnel considering the transitional Reynolds number regime. Three different configurations with varying distances between the fixed elastic axis and the variable center of gravity were considered. Additional free-oscillation tests in still air were carried out in order to make the mechanical properties of the setup available for the simulations. The present contribution describes the numerical methodology applied consisting of a partitioned coupled solver combining eddy-resolving large-eddy simulations on the fluid side with a solver for the governing equations of the translation and rotation of the rigid wing. In order to prove the parameters provided by the experiment and to determine the pure material damping coefficients not available from the measurements, simulations of 1-DOF free-oscillation tests in still air are carried out and analyzed. For validation purposes the corresponding 2-DOF free-oscillation tests in still air are assessed and a good agreement with the experimental data is achieved. Finally, the wing exposed to a constant free-stream of varying strength is analyzed leading to the characterization of complex instantaneous FSI phenomena such as limit-cycle oscillations and flutter. Under full utilization of the supplementary measurements the predictions are evaluated in detail. Contrary to the experiments the simulations provide the entire fluid data and unique data for the translatory and rotatory movement allowing to investigate the causes of the observed phenomena. Both limit-cycle oscillations and flutter can be reproduced by the coupled FSI predictions.     

A weighted least square scheme for compressible flows

The article describes the development of a high order finite volume method for the solution of transonic flow problems. The method is based on a reconstruction procedure similar to the weighted essentially non-oscillatory scheme (WENO). The analysis of accuracy and stability of the method is carried out for the case of smooth data and for simple discontinuity. The computational results demonstrate the performance of the WLSQR method for the solution of several flow problems in 2D and 3D using both structured and unstructured meshes.