Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier–Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations.     

Unsteady loading on an airfoil of arbitrary thickness

The unsteady loading on an airfoil of arbitrary thickness is evaluated by using the generalized form of Blasius theorem and a conformal mapping that maps the airfoil surface onto a circle. For a blade vortex interaction the results show that the time history of the unsteady loading is determined by the passage of the vortex relative to the leading edge singularity in the circle plane. The singularity lies inside the circle and moves to a smaller radius as the thickness is increased, causing the unsteady loading pulse to be smoothed. The effect of angle of attack is to move the stagnation point relative to the leading edge singularity and this significantly increases the unsteady lift if the vortex passes on the suction side of the airfoil. These characteristics are different for a step upwash gust, which is considered as a simplified model of a large scale turbulent gust. It is shown that the time history of the magnitude of the unsteady loading is almost completely unaltered by angle of attack for the step gust, but it's direction of action rotates forward by an angle equal to the angle of attack, extending an earlier result by Howe for a flat plate in a turbulent flow to airfoils of arbitrary thickness. However spectral analysis of the gust shows that the high frequency blade response is reduced as the thickness of the airfoil is increased.     

Acoustic wave motion along a narrow cylindrical duct in the presence of an axial mean flow and temperature gradient

A numerical solution is presented to the problem of nonisentropic acoustic wave motion in a circular capillary tube in the presence of both axial mean flow and a background axial temperature gradient. The effects of the radial components of the acoustic velocity are included in the analysis. The main application area is in the study of the acoustic effects of catalytic converters. The solution makes use of a series expansion and is valid for small relative changes in the background temperature, which are typical of this application area. Various solutions to the problem have been obtained previously, using different simplifications to the complete problem which is considered here. It is shown that each of the simplifications results in errors for the predicted attenuation of at least 20 dB/m, using conditions typical for catalytic converters. In particular, the isentropic assumption is shown to be invalid.     

Anomalous response of stratified fluid to forcing

The time-independent disturbances induced by nonuniformly distributed surface shear stress in a binary fluid (salt water) are analyzed in the linear approximation. It is shown that correct treatment of two scalar fields (stratified background temperature and salinity distributions) may lead to counterintuitive qualitative predictions even if the thermal and salt diffusivities are equal. In particular, when stable salinity stratification is imposed on stable temperature stratification, both the amplitude and depth of the disturbance may substantially increase rather than decrease (contrary to intuitive expectations). A previously unknown mechanism of convective instability is revealed for a stable density-stratified binary fluid.     

An expert system for predicting nonlinear aeroelastic behavior of an airfoil

In this paper we present an expert system to perform steady-state response predictions. We consider an aeroelastic model simulating a two degree-of-freedom airfoil oscillating in pitch and plunge with a freeplay nonlinearity in the pitch degree-of-freedom. In the proposed data-driven methodology, a freeplay is first confirmed, and then the locations of the switching points are determined. A state-space formulation is constructed to model the piece-wise linear system. The parameters of the system are estimated using the Kalman filter and the expectation maximization algorithm. The attractive feature of the present approach is its ability to accurately predict the steady-state behavior of the nonlinear aeroelastic system with freeplay, using only a limited amount of transient input data. To demonstrate the effectiveness of the proposed methodology, we present applications to freeplay aeroelastic data arising from wind tunnel experiments and numerical simulations.     

Acoustic susceptibility of an insulating spin-glass

High frequency acoustic measurements have been performed at temperatures around the freezing pointT _c in a cobalt insulating spin-glass. Assuming a Waller coupling mechanism between the spins and the acoustic wave, the data are interpreted in the framework of a dynamical model which takes into account the modulation of the reaction field. As a result, at the freezing temperature the characteristic relaxation time has no anomaly while the relevant susceptibility presents a maximum. The peculiar frequency dependence (as ^1/2) atT _c of the complex elastic constant is experimentally put in evidence.Associated with the Centre National de la Recherche Scientifique (UA 789)     

匀加速运动声源的声场建模及其数值算法研究

针对匀加速运动点声源的声场特性与其运动状态密切相关这一问题,提出匀加速直线运动状态下点声源的声场计算方法。利用此方法建立了匀加速直线运动时点声源的声压模型,对模型中的关键参数声矢量R进行数值解析,并对声压进行数值分析仿真,得出匀加速直线运动时固定接收点的声压数值计算方法。用此方法对固定接收点位置的匀加速点声源声压进行声场建模,结果表明:在声源接近接收者一定距离以后,声压明显增大;在此距离之外,距离对声压的影响不大。     

Lift and drag performances of an axisymmetric airfoil controlled by plasma actuator

A Dielectric Barrier Discharge (DBD) is mounted at the leading edge of a NACA 0015 airfoil model. The effects of steady and unsteady actuations on the lift and drag coefficients are investigated by time-averaged force measurements. Results demonstrate that the stall regime can be delayed of one or two degrees while the drag coefficient is reduced. The aerodynamic performances are enhanced for high voltage frequency coinciding with the natural vortex shedding frequency measured here by time-resolved PIV. The last part of the paper deals with a periodic excitation which improves the actuation efficiency.     

Acoustic characterisation of an impact forming machine

The quantification of the acoustic quality of an impact forming machine by a single parameter, such as the sound power, is usually inadequate. This is so since the sound power of such a machine can vary within wide limits depending on the levels of process variables selected in carrying out a forming operation. This paper describes the procedure of determining experimentally the sound power of a forming machine and discusses various aspects related to its acoustic quantification. The problems encountered in performing tests on a machine located in a general workshop, together with the relevance and limitations of sound power as an acoustic yardstick for machines creating transient noise, are also discussed.